JPH10126275A - Compressing method and expanding method, compressing program recording medium and expanding program recording medium, and compressing device and expanding device for linear time-series data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To widen the width of choices of compressing and expanding methods which compress and expand linear time-series data according to their characteristics by including processes from a process for inputting linear time-series data and its approximate precision to a process for outputting data on node candidates and data on time corresponding to them as compressed information. SOLUTION: In an input process P4a, the linear time-series data and its approximate precision value are inputted. In a node candidate calculating process P1a, node candidates for an interpolating function which approximates the linear time-series data are calculated. In a node position optimizing process P1b, the node candidates are moved to optimize node positions. In a deciding process P1c, the error between linear time-series data generated by the interpolating function, on the basis of the node candidates having the positions optimized and the original linear time-series data, is decided. In an output process P4b, the node candidate data and data on the time corresponding to them are outputted as compressed information.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a one-dimensional time-series data compression method, a one-dimensional time-series data expansion method, a one-dimensional time-series data compression program recording medium, a one-dimensional time-series data expansion program recording medium, and a one-dimensional time-series data expansion program. The present invention relates to a series data compression device and a one-dimensional time-series data decompression device, which belong to the field of signal processing technology, but include movement of a rigid articulated object, deformation of a mesh-like surface, and deformation of an elastic object. It can also be applied to time-series data describing such.

[0002]

2. Description of the Related Art In recent years, the development of the Internet has been remarkable. In the Internet, HTML (Hyper T
Since the Ext Makeup Language) can handle two-dimensional images and audio signals, the Internet can be used as a transmission medium for various multimedia information such as image information and audio information. However, this HTML can handle two-dimensional images, but cannot handle three-dimensional CG images. VRML (Virtual Reason) is a language that enables processing of three-dimensional images.
lity Modeling Language) has been proposed.

However, in VRML, it is difficult to represent a three-dimensional CG image showing the movement of a human. To realize this, a human is regarded as a rigid articulated object, and the position and the like of each joint are represented by time-series data. However, in this case, the amount of generated data becomes enormous. In order to avoid this data amount problem, multidimensional time-series data such as joint positions is decomposed into one-dimensional time-series data, and each one-dimensional time-series data is decomposed.
The compression may be performed for each dimensional time-series data.

[0004] As a method of compressing such one-dimensional time series data, a method generally applied is an orthogonal method such as discrete Fourier transform or discrete cosine transform, which is used when performing signal processing in acoustic engineering or the like. This is a method of compressing information using conversion.

References relating to this orthogonal transformation include “Speech”, edited by The Acoustical Society of Japan, Kazuo Nakata, Corona, 19
77 years. References for time series data of joint angles of rigid articulated objects include Unuma, M, et al., "Fo
urier Principles for Emotion-based Human Figure An
imation ", SIGGRAPH95 Proceedings, pp91-95, 1995.

In the method of compressing information using the orthogonal transform, first, given one-dimensional time-series data is converted to a discrete Fourier series expansion expression or a discrete cosine series expansion expression using data at all times. Convert to
Next, the amount of information is compressed by cutting high-frequency components of the transformed series expansion expression.

[0007]

The information can be expanded by applying an inverse Fourier transform or an inverse cosine transform to the information compressed using the orthogonal transform. At this time, as decompressed data, it is possible to generate not only the same number of data as the original data but also any number of data having a different number from the original data. Since the basis is a trigonometric function, its properties are reflected in the expanded data.

The present invention has been made to solve the above-mentioned problems of the prior art, and can perform compression and decompression in accordance with the properties of one-dimensional time-series data. Even if the number is different from the original data, the effects of the compression and decompression processes rarely affect the decompressed data, and compression is performed using the statistical properties of the data. Rather, it provides a new compression and decompression method that complements the existing compression method because it is a compression method that compresses data so that it is within the error range from the original data, which is specified at the time of compression. One-dimensional time-series data compression device, one-dimensional time-series data decompression device, one-dimensional time-series data compression method, one-dimensional time-series data decompression method that can expand the range of selection of compression and decompression methods , One-dimensional time system This invention was made in order to obtain a recording medium of a data compression program recording medium, and one-dimensional time series data decompression program.

[0009]

A one-dimensional time-series data compression method according to claim 1 of the present invention is a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its A first step of inputting approximation accuracy, a second step of calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data, and a third step of optimizing the position of the node candidate; A fourth step of determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data based on the node candidate whose position has been optimized; and If the value is determined to exceed the value based on the approximation precision, the number of nodes is changed, and the fifth step is returned to the second step. If it is determined not to exceed It is obtained to include a sixth step of outputting the data and information that has been compressed and the data at a time corresponding to the candidate.

A one-dimensional time-series data compression method according to a second aspect of the present invention is a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are input. A first step, a second step of determining whether the one-dimensional time-series data includes data within the approximation accuracy, and the approximation of the one-dimensional time-series data by the second step. A third step of calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data when it is determined that data within the accuracy is not included, and a fourth step of optimizing the position of the node candidate A fifth step of determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data based on the node candidate whose position has been optimized; and the fifth step The error is close to A sixth step of changing the number of nodes when it is determined to exceed the value based on the accuracy and returning to the third step, and a data within the approximation accuracy of the one-dimensional time-series data by the second step. Is output, information is output to the effect that the one-dimensional time-series data is data within the approximation accuracy, and the error does not exceed a value based on the approximation accuracy in the fifth step. And a seventh step of outputting the data of the node candidate and the data of the time corresponding to the node candidate as compressed information.

A one-dimensional time-series data compression method according to a third aspect of the present invention is a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are input. A first index for adding an index to the one-dimensional time-series data in the order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data.
And a second step of always including the start and end data from the one-dimensional time-series data, and randomly determining only a few node candidates, and an index number for the node candidates. Interpolation by an interpolation function as an independent variable to calculate an error from the original one-dimensional time-series data
And a fourth step of calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance. A fifth step of repeatedly changing node candidates so as to be the minimum to determine a sub-optimal node candidate, and interpolating the sub-optimal node candidate with the interpolation function to approximate the original one-dimensional time-series data. A sixth step of generating one-dimensional time-series data and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; A seventh step of calculating the value of the second objective function defined by the weighted addition of (a), and if the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy, an increment is added to the number of nodes. From the second step to the An eighth step of repeating the process up to the step, if the value of the second objective function is less than the threshold value,
A ninth step of outputting compressed data including the initial time and time interval of the one-dimensional time-series data, the finally determined index number of the node candidate, and the value of the node candidate. It was done.

A one-dimensional time-series data compression method according to a fourth aspect of the present invention is a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are input. A first index for adding an index to the one-dimensional time-series data in the order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data.
And a second step of determining, from the one-dimensional time-series data, node candidates of only a few nodes so as to always include start and end data and to be approximately equally spaced with respect to the index. And a third step of interpolating the node candidate with an interpolation function using an index number as an independent variable to calculate an error from the original one-dimensional time-series data;
A fourth step of calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance, and setting the value of the first objective function to be a minimum. A fifth step of repeatedly changing node candidates to determine a sub-optimal node candidate, and interpolating the sub-optimal node candidate by the interpolation function to approximate the original one-dimensional time-series data A sixth step of generating data and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; and, based on the error, adding a maximum value of the error, an error average, and an error variance. A seventh step of calculating the value of the second objective function defined in the above, and if the value of the second objective function is equal to or greater than the threshold value corresponding to the approximation accuracy, a value obtained by adding an increment to the number of nodes is added to a new The second to seventh steps are defined as the number of nodes. An eighth step of repeating the up process,
If the value of the second objective function is less than the threshold value, it is composed of the initial time and the time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate. And a ninth step of outputting compressed data.

A one-dimensional time-series data compression method according to a fifth aspect of the present invention is a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are input. A first step of adding an index to the one-dimensional time-series data in order of time and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; and an absolute value of the one-dimensional time-series data Is determined to be less than or equal to the approximation accuracy, and if less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output, and if not, the process proceeds to a third step described later. A second step, a third step of always including the start and end data from the one-dimensional time-series data, and randomly determining only a few node candidates, and an index of the node candidates. German number A fourth step of calculating an error from the original one-dimensional time-series data by interpolating using an interpolation function as a variable, and defining from the error the weighted addition of the maximum value of the error, the error average, and the error variance A fifth step of calculating the calculated value of the first objective function, and a sixth step of repeatedly changing the node candidates so as to minimize the value of the first objective function and determining a sub-optimal node candidate. Interpolating the suboptimal node candidates using the interpolation function to generate one-dimensional time-series data approximating the original one-dimensional time-series data, and generating an error between the one-dimensional time-series data and the original one-dimensional time-series data A seventh step of calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance; and The value of the objective function is equal to or less than the threshold value corresponding to the approximation accuracy. If, as a new number of nodes not containing added increment the number of nodes, the third
A ninth step of repeating the processing from the step to the eighth step, and if the value of the second objective function is less than the threshold value, the initial time and the time interval of the one-dimensional time-series data are finally determined. And a tenth step of outputting compressed data composed of the index numbers of the selected node candidates and the values of the node candidates.

A one-dimensional time-series data compression method according to a sixth aspect of the present invention is a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are input. A first step of adding an index to the one-dimensional time-series data in order of time and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; and an absolute value of the one-dimensional time-series data Are determined to be all less than or equal to the approximation accuracy. If the accuracy is less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output, and if not, the process proceeds to a third step described later. And a third step of determining, from the one-dimensional time-series data, the node candidates of only a few nodes so as to always include the beginning and end data and to be approximately equally spaced with respect to the index. Process and A fourth step of interpolating the node candidate by an interpolation function using an index number as an independent variable to calculate an error with the original one-dimensional time-series data; and, from the error, a maximum value of the error and an error average. A fifth step of calculating the value of the first objective function defined by weighted addition with the error variance, and repeatedly changing the node candidates so that the value of the first objective function is minimized; And generating the one-dimensional time-series data approximating the original one-dimensional time-series data by interpolating the sub-optimal node candidates using the interpolation function. A seventh step of calculating an error from the one-dimensional time-series data, and calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance Eighth step and the second step If the value of the function is equal to or greater than the threshold value corresponding to the approximation accuracy, a ninth step of repeating the processing from the third step to the eighth step by setting the value obtained by adding an increment to the number of nodes as a new number of nodes And if the value of the second objective function is less than the threshold, the initial time and the time interval of the one-dimensional time series data, the index number of the finally determined node candidate, and the value of the node candidate And a tenth step of outputting the compressed data thus obtained.

According to a seventh aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the calculation of the sub-optimal node candidate is performed in the one-dimensional time-series data compression method. For the index of the node candidate,
Numbered in ascending order is I (j), 0 ≤
When j ≦ m, if the relationship of I (j-1) <I (j) -1 holds, the first candidate when the node candidate I (j) is replaced with the node candidate I (j) -1 The value of the objective function is calculated, a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I (j) -1 Then, set ΔE (1-) to 0,
If the relationship of I (j) +1 <I (j + 1) holds, the node candidate I
calculating the value of the first objective function when (j) is replaced with the node candidate I (j) +1, and calculating the original first value from the value of the first objective function.
Calculate a value ΔE (1+) obtained by subtracting the value of the objective function, and obtain I (j) + 1 ≧ I
If (j + 1), the ΔE (1+) is set to 0, and the ΔE (1-) <0
And if the relationship ΔE (1+) ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1
-) ≧ 0 and the relationship ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the Δ
If the relationship of E (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0
And the relationship of ΔE (1 +) <0 holds, and ΔE (1+
If-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the Δ
The relationship of E (1 +) <0 holds, and the ΔE (1-) is the ΔE
If it is larger than (1+), the operation of exchanging the node candidate I (j) with the node candidate I (j) +1 is performed in the order of small to large for odd j, and large for even j. If the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is repeated for odd j. Are performed again in ascending order from the smallest to the largest, and for even j, in the order from the largest to the smallest, and whether the node candidates have not been exchanged at all or whether the value of the first objective function is the original first objective function If the value is larger than the value obtained by subtracting the threshold value from the value of, the processing is terminated to terminate the processing.

The one-dimensional time-series data compression method according to claim 8 of the present invention is the one-dimensional time-series data compression method according to any one of claims 3 to 6, wherein the suboptimal node candidate calculation is For the index of the node candidate,
Numbered in ascending order is I (j), 0 ≤
When j ≦ m, if the relation of I (j-1) <I (j) -1 holds, the first candidate when the node candidate I (j) is replaced with the node candidate I (j) -1 The value of the objective function is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I (j) -1 If the relationship holds, then ΔE
(1-) is set to 0, and when the relationship of I (j) +1 <I (j + 1) holds, the above-mentioned node candidate I (j) is replaced with the node candidate I (j) +1 The value of the first objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function
If the relationship of I (j) + 1 ≧ I (j + 1) holds, ΔE (1+) is set to 0, ΔE (1-) <0 and ΔE (1
+) ≧ 0, the node candidate I (j) is replaced with the node candidate I (j) -1, and the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 is satisfied. Is satisfied, the node candidate I (j) is replaced with the node candidate I (j) + 1.If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 is satisfied, the node Candidate I
(j) is not exchanged, the ΔE (1-) <0 and the ΔE (1+)
<0, and ΔE (1-) is equal to ΔE (1
+) If below, the node candidate I (j) is replaced by the node candidate I (j)-
If the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and if ΔE (1-) is larger than ΔE (1+), The node candidate I (j) is replaced with the node candidate I (j).
The operation of exchanging +1 is performed in the order of large to small for odd j, and in the order of small to large for even j. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operation is performed using an odd j
Are performed again in the order of large to small, and for even j, in the order of small to large, and whether or not the exchange of the node candidates has been performed at all,
If the value of the first objective function is greater than the value of the original first objective function minus a threshold value, the processing is terminated to terminate the processing.

According to a ninth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the calculation of the sub-optimal node candidate is performed by using For the index of the node candidate,
Numbered in ascending order is I (j), 0 ≤
When j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the first objective when node candidate I (j) is replaced with node candidate I (j) -1 Calculating a value of the function, calculating a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function,
If the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original first objective function is subtracted from the value of the first objective function. ΔE (1+)
If the relationship of + 1 ≧ I (j + 1) holds, set ΔE (1+) to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, The node candidate I (j) is converted to the node candidate I (j) -1.
If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is replaced with the node candidate I (j).
If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged and the ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds, and if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1. And replace the Δ
E (1-) <0 and the relationship of ΔE (1 +) <0 holds, and
If the ΔE (1-) is larger than the ΔE (1+), the operation of replacing the candidate node I (j) with the candidate node I (j) +1 is j = 1.
To [m / 2], and from j = m-1 to [m / 2] +1, and the value of the first objective function at the end of the series of processes is the value of the original first objective function. If the value is equal to or less than the value obtained by subtracting the threshold from the value, the operation is performed from j = 1 to [m / 2].
And j = m-1 to [m / 2] +1 again, and whether the node candidates have not been exchanged at all or the value of the first objective function is a threshold value from the value of the original first objective function If the value is larger than the value obtained by subtracting, by ending the processing,
It is something to do.

According to a tenth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the calculation of the sub-optimal node candidate is performed in the one-dimensional time-series data compression method. The index of the node candidate index, which is numbered in ascending order, is I (j),
When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. 1) calculate the value of the objective function, calculate the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, and obtain I (j-1) ≧ I (j) − If the relationship of 1 holds, the above ΔE (1
-) Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first node when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1 ), The above-mentioned ΔE (1
+) Is set to 0, ΔE (1-) <0 and ΔE (1+) ≧ 0
If the relationship holds, the node candidate I (j) is replaced with the node candidate I (j) -1, the ΔE (1-) ≧ 0 and the ΔE (1+)
<0, the candidate node I (j) is replaced with the candidate node I (j) +1, and ΔE (1-) ≧ 0 and ΔE
If the relationship of (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE If (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1+ ) <0 and if ΔE (1-) is greater than ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 = [M / 2] to 1 and j = [m / 2] +1
m−1, and if the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is performed by j = [m / 2] to 1 and j = [m / 2] +1 to m-1 again, and whether the exchange of the node candidates has not been performed at all,
If the value of the first objective function is greater than the value of the original first objective function minus a threshold value, the processing is terminated to terminate the processing.

The one-dimensional time-series data compression method according to claim 11 of the present invention is the one-dimensional time-series data compression method according to any one of claims 3 to 6, wherein the suboptimal node candidate calculation is performed by: The index of the node candidate index, which is numbered in ascending order, is I (j),
When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. 1) calculate the value of the objective function, calculate the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, and obtain I (j-1) ≧ I (j) − If the relationship of 1 holds, the above ΔE (1
-) Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first node when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1 ), The above-mentioned ΔE (1
+) Is set to 0, ΔE (1-) <0 and ΔE (1+) ≧ 0
If the relationship holds, the node candidate I (j) is replaced with the node candidate I (j) -1, the ΔE (1-) ≧ 0 and the ΔE (1+)
<0, the candidate node I (j) is replaced with the candidate node I (j) +1, and ΔE (1-) ≧ 0 and ΔE
If the relationship of (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the relationship of ΔE If (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1+ ) <0, and if ΔE (1-) is greater than ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 = 1 to m−1, and if the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is performed by j =
1 to m-1 again in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is greater than the value of the original first objective function minus a threshold, The processing is performed by terminating the processing.

According to a twelfth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the calculation of the sub-optimal node candidate is performed by using the node For the candidate index,
Numbered in ascending order is I (j), 0 ≤
When j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the first objective when node candidate I (j) is replaced with node candidate I (j) -1 Calculating the value of the function, calculating a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function,
If the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original first objective function is subtracted from the value of the first objective function. ΔE (1+)
If the relationship of + 1 ≧ I (j + 1) holds, set ΔE (1+) to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, The node candidate I (j) is converted to the node candidate I (j) -1.
If the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j).
+1, if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds, and if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) becomes the node candidate I (j) -1. Replace the ΔE
(1-) <0 and the relationship of ΔE (1 +) <0 holds, and if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is replaced with the node candidate. The operation of replacing I (j) +1 with j = m-1
To 1 in order, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the above operation is performed from j = m-1. Steps are repeated until 1 and the node candidates are not exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the process ends. By doing so, it is done.

According to a thirteenth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the calculation of the sub-optimal node candidate is performed in the one-dimensional time-series data compression method. The index of the node candidate index, which is numbered in ascending order, is I (j),
When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. 1) calculate the value of the objective function, calculate a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, and obtain I (j-1) ≧ I (j) − If the relationship of 1 holds, the above ΔE (1
-) Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first node when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1 ), The above-mentioned ΔE (1
+) Is set to 0, ΔE (1-) <0 and ΔE (1+) ≧ 0
Is satisfied, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function and the value of the original first objective function at the time of this exchange are performed. When the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is exchanged for the node candidate I (j) +1, and The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the Δ
If the relationship of E (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0
And the relationship of ΔE (1 +) <0 holds, and ΔE (1+
If −) is equal to or less than ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) −1, and the value of the first objective function and the element at the time of the exchange are exchanged. The values of the first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold, and ΔE (1-) is larger than ΔE (1+). Then, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function and the value of the original first objective function at the time of the exchange are exchanged. The exchange operation is performed in the order of small to large for the odd j, and in the order of large to small for the even j, and the value of the first objective function at the time when these series of processing is completed is changed to the original value. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the first objective function, the above-described operation is performed in the order of small to large for odd j, and for even j. Is performed again in ascending order from the largest to the smallest, and if the exchange of the node candidates has not been performed at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, The processing is performed by terminating the processing.

According to a fourteenth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the calculation of the sub-optimal node candidate is performed by using I (j), 0 ≤j
≤m, if the relation I (j-1) <I (j) -1 holds, the first objective function when node candidate I (j) is replaced with node candidate I (j) -1 , And a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated.
If the relationship of (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, The first when node candidate I (j) is replaced with node candidate I (j) +1
The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated.
If the relationship of (j) + 1 ≧ I (j + 1) holds, ΔE (1+) is set to 0, and the relationship of ΔE (1-) <0 and ΔE (1+) ≧ 0 is satisfied. If this holds, the node candidate I (j) is replaced with the node candidate I
(j) -1 and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged.
If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is exchanged for the node candidate I (j) +1, and at the time of this exchange. The value of the first objective function is exchanged with the value of the original first objective function, and ΔE (1-) ≧
0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidates I (j) are not exchanged, and the relationships of ΔE (1-) <0 and ΔE (1 +) <0 hold. And if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I (j) is replaced with the node candidate
I (j) -1 and exchange the value of the first objective function at the time of the exchange with the value of the original first objective function,
The relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is performed in the order of large to small for odd j, and in the order of small to large for even j. If the value of the first objective function at the time of the end is less than or equal to the value of the original first objective function minus the threshold,
The above operation is performed again in the order of large to small for odd j, and in the order of small to large for even j, and whether the node candidates have not been exchanged at all or the value of the first objective function is If the value is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, the processing is terminated to make the determination.

According to a fifteenth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the calculation of the sub-optimal node candidate is performed by using the node Candidate indices are numbered in ascending order as I (j), 0 ≦ j
≤m, if the relationship I (j-1) <I (j) -1 holds, the first objective function when node candidate I (j) is replaced with node candidate I (j) -1 Is calculated by subtracting the original value of the first objective function from the value of the first objective function, and ΔE (1-) is calculated.
If the relationship (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) was replaced with the node candidate I (j) +1 was calculated, and the value of the original first objective function was subtracted from the value of the first objective function. The value ΔE (1+) is calculated and I (j)
If the relationship of + 1 ≧ I (j + 1) holds, set ΔE (1+) to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, The node candidate I (j) is converted to the node candidate I (j) -1.
The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the Δ
If the relationship of E (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the node candidate at the time of the exchange is exchanged. The value of one objective function and the value of the original first objective function are exchanged. If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate
Without exchanging I (j), the ΔE (1-) <0 and the ΔE (1+)
<0, and the ΔE (1-) is the ΔE (1+)
If below, the node candidate I (j) is replaced by the node candidate I (j) -1.
The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the Δ
If the relationship of E (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is greater than the ΔE (1+), the node candidate I (j) is The operation of exchanging for the candidate I (j) +1 and exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function is from j = 1 to [m / 2]. , And from j = m-1 to [m / 2] +1, and the value of the first objective function at the time when these series of processing is completed is obtained by subtracting the threshold value from the value of the original first objective function. If less than
The above operation is performed again in order from j = 1 to [m / 2] and from j = m-1 to [m / 2] +1, and it is determined whether the exchange of the node candidates has not been performed at all or the first objective function. Is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, the processing is terminated to make the determination.

A one-dimensional time-series data compression method according to claim 16 of the present invention is the one-dimensional time-series data compression method according to any one of claims 3 to 6, wherein the calculation of the sub-optimal node candidate is performed at the node I (j), 0 ≤j
≤m, if the relationship I (j-1) <I (j) -1 holds, the first objective function when node candidate I (j) is replaced with node candidate I (j) -1 Is calculated by subtracting the original value of the first objective function from the value of the first objective function, and ΔE (1-) is calculated.
If the relationship (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) was replaced with the node candidate I (j) +1 was calculated, and the value of the original first objective function was subtracted from the value of the first objective function. The value ΔE (1+) is calculated and I (j)
If the relationship of + 1 ≧ I (j + 1) holds, set ΔE (1+) to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, The node candidate I (j) is converted to the node candidate I (j) -1.
The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the Δ
If the relationship of E (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the node candidate at the time of the exchange is exchanged. The value of one objective function and the value of the original first objective function are exchanged. If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate
Without exchanging I (j), the ΔE (1-) <0 and the ΔE (1+)
<0, and the ΔE (1-) is the ΔE (1+)
If below, the node candidate I (j) is replaced by the node candidate I (j) -1.
The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the Δ
If the relationship of E (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is greater than the ΔE (1+), the node candidate I (j) is The operation of exchanging the candidate I (j) +1 and exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function is from j = [m / 2] to 1, And j = [m / 2] +1 to m−1 in order, and the value of the first objective function at the time when these series of processing ends is the first original function.
If the value is equal to or less than the value of the objective function minus the threshold, the operation is performed from j = [m / 2] to 1 and j = [m / 2] +1 to m−
1 until the node candidates have not been exchanged at all, or if the value of the first objective function is
If it is greater than the value of the objective function minus the threshold,
The processing is performed by terminating the processing.

According to a seventeenth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the calculation of the sub-optimal node candidate is performed by using I (j), 0 ≤j
≤m, if the relationship I (j-1) <I (j) -1 holds, the first objective function when node candidate I (j) is replaced with node candidate I (j) -1 Is calculated by subtracting the original value of the first objective function from the value of the first objective function, and ΔE (1-) is calculated.
If the relationship (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) was replaced with the node candidate I (j) +1 was calculated, and the value of the original first objective function was subtracted from the value of the first objective function. The value ΔE (1+) is calculated and I (j)
If the relationship of + 1 ≧ I (j + 1) holds, set ΔE (1+) to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, The node candidate I (j) is converted to the node candidate I (j) -1.
The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the Δ
If the relationship of E (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the node candidate at the time of the exchange is exchanged. The value of one objective function and the value of the original first objective function are exchanged. If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate
Without exchanging I (j), the ΔE (1-) <0 and the ΔE (1+)
<0, and the ΔE (1-) is the ΔE (1+)
If below, the node candidate I (j) is replaced by the node candidate I (j) -1.
The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the Δ
If the relationship of E (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is greater than the ΔE (1+), the node candidate I (j) is The operation of exchanging the candidate I (j) +1 and exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function is sequentially performed from j = 1 to m-1. If the value of the first objective function at the end of the series of processes is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operations are repeated again from j = 1 to m-1. If the exchange of the node candidates has not been performed at all or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is terminated. It is like that.

The one-dimensional time-series data compression method according to claim 18 of the present invention is the one-dimensional time-series data compression method according to any one of claims 3 to 6, wherein the calculation of the sub-optimal node candidate is performed at the node I (j), 0 ≤j
≤m, if the relationship I (j-1) <I (j) -1 holds, the first objective function when node candidate I (j) is replaced with node candidate I (j) -1 Is calculated by subtracting the original value of the first objective function from the value of the first objective function, and ΔE (1-) is calculated.
If the relationship (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) was replaced with the node candidate I (j) +1 was calculated, and the value of the original first objective function was subtracted from the value of the first objective function. The value ΔE (1+) is calculated and I (j)
If the relationship of + 1 ≧ I (j + 1) holds, set ΔE (1+) to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, The node candidate I (j) is converted to the node candidate I (j) -1.
The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the Δ
If the relationship of E (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the node candidate at the time of the exchange is exchanged. The value of one objective function and the value of the original first objective function are exchanged. If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate
Without the exchange of I (j), the relationships of ΔE (1-) <0 and ΔE (1 +) <0 hold, and ΔE (1
If-) is equal to or smaller than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original If the value of the first objective function is exchanged, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and if the ΔE (1-) is greater than the ΔE (1+) For example, the node candidate I (j) is replaced with the node candidate I (j) +1, and the exchange of the value of the first objective function and the value of the original first objective function at the time of the exchange is performed. J = m-
Steps from 1 to 1 are performed in order. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operation is performed by j = m-1 From 1
Until the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is terminated. This is done by

According to a nineteenth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the number of node candidates finally determined is reduced. If not more than the number of data that was not a candidate, output compressed data consisting of an identifier indicating the node candidate, the index number of the finally determined node candidate and the value of the node candidate, If the finally determined number of node candidates is larger than the number of data that did not become the candidate, it is composed of an identifier that is not a node candidate, the index number of the data that did not become the node candidate, and the value of the node candidate. The compressed data thus output is output.

A one-dimensional time-series data compression method according to claim 20 of the present invention is the one-dimensional time-series data compression method according to any one of claims 1 to 6, wherein For data, the one-dimensional time-series data compression method is independently applied to time and data, and each is compressed independently.

According to a twenty-first aspect of the present invention, there is provided a one-dimensional time-series data compression method according to any one of the first to sixth aspects, wherein the one-dimensional time-series data compression method comprises the steps of: Multi-dimensional time-series data is compressed by repeatedly applying the one-dimensional time-series data compression method to each one-dimensional time-series data.

A one-dimensional time-series data compression method according to claim 22 of the present invention is the one-dimensional time-series data compression method according to any one of claims 1 to 6, wherein For the data, the approximation accuracy value is increased in order from the one-dimensional time-series data of the propagation source, and
By repeatedly applying the dimensional time series data compression method,
All of the one-dimensional time-series data is compressed.

According to a twenty-third aspect of the present invention, there is provided a one-dimensional time-series data decompression method for decompressing compressed data compressed by the one-dimensional time-series data compression method according to any one of the first to third aspects. A first step of inputting compressed compressed data and the number of data when decompressing the compressed data;
By interpolating the compressed data using the same interpolation function as that used in the compression, the same number of data as the number of data is calculated, and the time is calculated from the initial time and the time interval by the same number as the number of data. And a third step of outputting the data and the time calculated in the second step.
And the step of

According to a twenty-fourth aspect of the present invention, there is provided a one-dimensional time-series data decompression method for decompressing compressed data compressed by the one-dimensional time-series data compression method according to any one of the second, fifth and sixth aspects. A first step of inputting compressed compressed data and the number of data when decompressing the compressed data;
When an identifier indicating that all the data is 0 is given to the compressed data, the time is calculated from the initial time and the time interval by the same number of 0s as the number of data, and 0 as the number of data. In the case where the compressed data is not provided with an identifier indicating that the data is all 0, the compressed data is interpolated using the same interpolation function as the interpolation function used in the compression. A second step of calculating the same number of data as the number and calculating the time from the initial time and the time interval by the same number as the data number; and outputting the data and the time calculated in the second step. And a third step.

According to a twenty-fifth aspect of the present invention, there is provided the one-dimensional time-series data decompression method according to the twenty-third or twenty-fourth aspect, wherein a plurality of compressed multi-dimensional time-series data constituting the compressed multi-dimensional time-series data are provided. The compressed one-dimensional time-series data is expanded by repeatedly applying the one-dimensional time-series data expansion method to each of the obtained one-dimensional time-series data.

A one-dimensional time-series data compression program recording medium according to claim 26 of the present invention is a medium in which a one-dimensional time-series data compression program at a uniform time interval is recorded, wherein said one-dimensional time-series data and its one-dimensional time series data compression program are recorded. A first step of inputting approximation accuracy, a second step of calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data, and a third step of optimizing the position of the node candidate; A fourth step of determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data based on the node candidate whose position has been optimized; and If the value is determined to exceed the value based on the approximation accuracy, the number of nodes is changed and the process returns to the second process. Not exceed It is those in which so as to record the one-dimensional time series data compression program comprising a sixth step of outputting the data and information that has been compressed and the data at a time corresponding thereto of the node candidates when the.

A one-dimensional time-series data compression program recording medium according to a twenty-seventh aspect of the present invention is a medium on which a one-dimensional time-series data compression program at an equal time interval is recorded. A first step of inputting approximation accuracy, and a second step of determining whether the one-dimensional time-series data includes data within the approximation accuracy.
And calculating a candidate node for an interpolation function that approximates the one-dimensional time-series data when it is determined in the second step that the one-dimensional time-series data does not include data within the approximation accuracy. A third step of optimizing the position of the node candidate, a fourth step of optimizing the position of the node candidate, and the one-dimensional time series data generated by the interpolation function based on the node candidate having the optimized position. A fifth step of determining an error from the series data, and if the fifth step determines that the error exceeds a value based on the approximation accuracy, the number of nodes is changed, and the process returns to the third step. In the sixth step and the second step, when it is determined that the one-dimensional time-series data includes data within the approximation accuracy, the one-dimensional time-series data is data within the approximation accuracy. Output information to the effect that A seventh step of outputting, as compressed information, the node candidate data and the corresponding time data when it is determined in the fifth step that the error does not exceed the value based on the approximation accuracy; And a one-dimensional time-series data compression program including the following.

A one-dimensional time-series data compression program recording medium according to a twenty-eighth aspect of the present invention is a medium in which a one-dimensional time-series data compression program at a uniform time interval is recorded. A first step of inputting approximation accuracy, adding an index to the one-dimensional time-series data in order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; A second step of always including the start and end data from the one-dimensional time-series data and randomly determining only a few node candidates, and interpolating the node candidates using index numbers as independent variables. Interpolated by the function, the original 1
A third step of calculating an error from the dimensional time-series data; and a fourth step of calculating a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance from the error. And a fifth step of repeatedly changing node candidates so as to minimize the value of the first objective function to determine a sub-optimal node candidate, and interpolating the sub-optimal node candidate by the interpolation function. A sixth step of generating one-dimensional time-series data that approximates the original one-dimensional time-series data and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; A seventh step of calculating a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance, wherein the value of the second objective function is equal to or greater than a threshold corresponding to the approximation accuracy. Then, add the increment to the number of nodes An eighth step of repeating the processing from the second step to the seventh step using the number of nodes, and an initial time of the one-dimensional time-series data if the value of the second objective function is less than the threshold. And a ninth step of outputting compressed data composed of the index number of the node candidate finally determined and the value of the node candidate.
The program stores a dimensional time-series data compression program.

A one-dimensional time-series data compression program recording medium according to claim 29 of the present invention is a medium in which a one-dimensional time-series data compression program at an equal time interval is recorded, wherein said one-dimensional time-series data and its one-dimensional data are recorded. A first step of inputting approximation accuracy, adding an index to the one-dimensional time-series data in order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; A second step of determining node candidates of only a few nodes so as to always include start and end data from one-dimensional time-series data and to be approximately equally spaced with respect to the index; A third step of interpolating the candidate by an interpolation function using an index number as an independent variable to calculate an error from the original one-dimensional time-series data; A fourth step of calculating the value of the first objective function defined by weighted addition of the error average and the error variance, and repeatedly changing the node candidates so that the value of the first objective function is minimized; A fifth step of determining an optimal node candidate, and interpolating the sub-optimal node candidate by the interpolation function to generate one-dimensional time series data approximating the original one-dimensional time series data; A sixth step of calculating an error between the data and the original one-dimensional time-series data, and from the error, a value of a second objective function defined by weighted addition of a maximum value of the error, an error average, and an error variance A step of calculating the second objective function, if the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy, a new number of nodes is obtained by adding an increment to the number of nodes, Eighth step of repeating the processing of the seventh step The second
If the value of the objective function is less than the threshold, the compressed data composed of the initial time and the time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate A one-dimensional time-series data compression program including a ninth step of outputting is recorded.

A one-dimensional time-series data compression program recording medium according to claim 30 of the present invention is a medium on which a one-dimensional time-series data compression program at an equal time interval is recorded. A first step of inputting approximation accuracy, adding an index to the one-dimensional time-series data in order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; It is determined whether or not the absolute values of the time-series data are all less than or equal to the approximation accuracy. If the absolute values are less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output and the process is terminated. A second step of shifting to the step of (1), and a third step of always including, from the one-dimensional time-series data, start and end data, and randomly determining only a few node candidates. A fourth step of calculating an error from the original one-dimensional time-series data by interpolating the node candidate using an interpolation function having an index number as an independent variable; A fifth step of calculating a value of a first objective function defined by weighted addition of error and error variance; and repeatedly changing node candidates so that the value of the first objective function is minimized. A sixth step of determining a candidate, and interpolating the sub-optimal node candidate using the interpolation function to generate one-dimensional time-series data approximating the original one-dimensional time-series data; A seventh step of calculating an error from the one-dimensional time-series data, and calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance An eighth step, the second object Is equal to or greater than the threshold value corresponding to the approximation accuracy, a ninth step of repeating the processing from the third step to the eighth step by setting the value obtained by adding an increment to the number of nodes as a new number of nodes; , The second
If the value of the objective function is less than the threshold, the compressed data composed of the initial time and the time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate A one-dimensional time-series data compression program including a tenth step of outputting is recorded.

A one-dimensional time-series data compression program recording medium according to a thirty-first aspect of the present invention is a medium on which a one-dimensional time-series data compression program is recorded at regular intervals of time, wherein the one-dimensional time-series data and its one-dimensional time series data compression program are recorded. A first step of inputting approximation accuracy, adding an index to the one-dimensional time-series data in order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; It is determined whether or not the absolute values of the time-series data are all less than or equal to the approximation accuracy. If the absolute values are less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output and the process is terminated. A second step of shifting to a step, and the steps of the one-dimensional time-series data including the start and end data, and including the nodes so as to be approximately equally spaced with respect to the index. A third step of deciding a candidate for the node, and a fourth step of calculating an error from the original one-dimensional time-series data by interpolating the candidate node with an interpolation function using an index number as an independent variable; A fifth step of calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance;
A sixth step of repeatedly changing node candidates so that the value of the first objective function is minimized and determining a sub-optimal node candidate; and interpolating the sub-optimal node candidate by the interpolation function to obtain the original A seventh step of generating one-dimensional time-series data approximating the one-dimensional time-series data and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; An eighth step of calculating the value of the second objective function defined by weighted addition of the maximum value, the error average, and the error variance, and if the value of the second objective function is equal to or greater than a threshold corresponding to the approximation accuracy, A ninth step of repeating the processing from the third step to the eighth step by adding an increment to the number of nodes to a new number of nodes, and if the value of the second objective function is less than the threshold, , Initial time and time interval of the one-dimensional time-series data A one-dimensional time-series data compression program including a tenth step of outputting compressed data composed of the finally determined index of the node candidate and the value of the node candidate. is there.

The one-dimensional time-series data compression program recording medium according to the thirty-second aspect of the present invention provides the one-dimensional time-series data compression program recording medium.
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (11), the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order of I (j) , 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. The value of the first objective function is calculated, a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I (j )
If -1, the ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) is set to the node candidate I (j).
The value of the first objective function at the time of replacement with +1 is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated. j) + 1 ≧ I (j + 1) if ΔE
(1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) ≧ 0 and the ΔE
If the relationship of (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 If the relationship holds, the node candidate I (j)
Are not exchanged, the ΔE (1-) <0 and the ΔE (1 +) <0
Holds, and if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j). The operation of exchanging +1 for odd j is performed in ascending order from small to large and for even j is performed in ascending order from large to small.
If the value of the objective function is equal to or less than the value of the original first objective function minus the threshold, the operation is performed in the order of small to large for odd j, and large to small for even j. Are performed again in the order of the node candidates.
If the value of the objective function is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the program to be executed is recorded by terminating the processing.

The one-dimensional time-series data compression program recording medium according to the thirty-third aspect of the present invention is the twenty-eighth to the third aspect.
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (11), the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order of I (j) , 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. The value of the first objective function is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I
If the relationship (j) -1 holds, the ΔE (1-) is set to 0.If the relationship I (j) +1 <I (j + 1) holds, the node candidate I (j) is set. The value of the first objective function when the node is replaced with the candidate node I (j) +1 is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function And I (j) +1
If the relationship ≧ I (j + 1) holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node The candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is The node candidate I (j) +1
If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0 and the If the relationship of ΔE (1 +) <0 holds and the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1. And the Δ
E (1-) <0 and the relationship of ΔE (1 +) <0 holds, and
If the ΔE (1-) is larger than the ΔE (1+), the operation of exchanging the node candidate I (j) with the node candidate I (j) +1 starts with the operation for the odd j, which is larger. The order of small ones and even j are performed in the order of small to large, and the value of the first objective function when these series of processes are completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function. Then, the above operation is performed again in the order of large to small for the odd j and in the order of small to large for the even j, and whether the exchange of the node candidates has not been performed at all or whether the first objective function Is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, the program to be executed is recorded by terminating the processing.

The one-dimensional time-series data compression program recording medium according to claim 34 of the present invention is characterized by claims 28 to 3
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (11), the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order of I (j) , 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. The value of the first objective function is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I (j) If the relationship of -1 holds, the above ΔE (1-) is set to 0, and I (j)
If the relationship of +1 <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the function is calculated. If the relationship of I (j) + 1 ≧ I (j + 1) holds, the value ΔE (1+ ) Is set to 0, and ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) ≧ 0 And if the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, ΔE (1-) ≧ 0 and ΔE (1+ ) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1
-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I
(j) is replaced with the node candidate I (j) -1, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold, and the ΔE (1
-) Is greater than ΔE (1+), the node candidate I
The operation of replacing (j) with the node candidate I (j) +1 is performed from j = 1 to [m
/ 2], and from j = m-1 to [m / 2] +1, and the value of the first objective function when these series of processes are completed is calculated from the value of the original first objective function. If less than or equal to the reduced threshold, repeat the operation from j = 1 to [m / 2], and
j = m-1 to [m / 2] +1, and the node candidates are not exchanged at all, or the value of the first objective function is set to a threshold from the value of the original first objective function. If it is larger than the subtracted one, the program to be executed is recorded by terminating the processing.

The one-dimensional time-series data compression program recording medium according to claim 35 of the present invention is characterized by claims 28 to 3
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (11), the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order of I (j) , 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. The value of the first objective function is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I (j) If the relationship of -1 holds, the above ΔE (1-) is set to 0, and I (j)
If the relationship of +1 <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the function is calculated. If the relationship of I (j) + 1 ≧ I (j + 1) holds, the value ΔE (1+ ) Is set to 0, and ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) ≧ 0 And if the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, the ΔE (1-) ≧ 0 and the ΔE (1+ ) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1
-) <0 and the relationship of ΔE (1 +) <0 holds, and if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j)
Is replaced with the node candidate I (j) -1, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 is satisfied, and the ΔE (1-) is the ΔE (1+) If it is greater, the operation of exchanging the node candidate I (j) for the node candidate I (j) +1 is from j = [m / 2] to 1 and j = [m / 2] +1 to m -1. If the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is performed by j = [m / 2] to 1 and j = [m /
2] The steps are repeated again from +1 to m−1, and no exchange of the node candidates is performed at all, or the value of the first objective function is larger than the value obtained by subtracting a threshold value from the value of the original first objective function. Then, the program to be executed is recorded by terminating the processing.

The one-dimensional time-series data compression program recording medium according to the thirty-sixth aspect of the present invention is the twenty-eighth to thirty-eighth aspect.
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (11), the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order of I (j) , 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. The value of the first objective function is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I (j) If the relationship of -1 holds, the above ΔE (1-) is set to 0, and I (j)
If the relationship of +1 <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the function is calculated. If the relationship of I (j) + 1 ≧ I (j + 1) holds, the value ΔE (1+ ) Is set to 0, and ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) ≧ 0 And if the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, the ΔE (1-) ≧ 0 and the ΔE (1+ ) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1
-) <0 and the relationship of ΔE (1 +) <0 holds, and if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j)
Is replaced with the node candidate I (j) -1, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and the ΔE (1-) is the ΔE (1+) If it is larger, the operation of exchanging the node candidate I (j) for the node candidate I (j) +1 is performed in order from j = 1 to m-1. If the value of the function is equal to or less than the value of the original first objective function minus the threshold, the operation is performed again in order from j = 1 to m−1, and whether the exchange of the node candidates has not been performed at all, If the value of the first objective function is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the program to be executed is recorded by terminating the processing.

The one-dimensional time-series data compression program recording medium according to the thirty-seventh aspect of the present invention is the thirty-eighth to thirty-eighth aspect.
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (11), the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order of I (j) , 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. The value of the first objective function is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I (j) If the relationship of -1 holds, the above ΔE (1-) is set to 0, and I (j)
If the relationship of +1 <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the function is calculated. If the relationship of I (j) + 1 ≧ I (j + 1) holds, the value ΔE (1+ ) Is set to 0, and ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) ≧ 0 And if the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, the ΔE (1-) ≧ 0 and the ΔE (1+ ) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1
-) <0 and the relationship of ΔE (1 +) <0 holds, and if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j)
Is replaced with the node candidate I (j) -1, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and the ΔE (1-) is the ΔE (1+) If it is larger, the operation of exchanging the node candidate I (j) for the node candidate I (j) +1 is performed in order from j = m-1 to 1, and the first object when a series of these processes is completed. If the value of the function is equal to or less than the value of the original first objective function minus the threshold, the above operation is repeated again from j = m-1 to 1, and whether or not the exchange of the node candidates has been performed at all, If the value of the first objective function is larger than a value obtained by subtracting a threshold value from the value of the original first objective function, a program to be executed by terminating the processing is recorded.

The one-dimensional time-series data compression program recording medium according to the thirty-eighth aspect of the present invention is the thirty-eighth to thirty-eighth aspect.
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (11), the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order of I (j) , 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. The value of the first objective function is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I (j) If the relationship of -1 holds, the above ΔE (1-) is set to 0, and I (j)
If the relationship of +1 <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the function is calculated. If the relationship of I (j) + 1 ≧ I (j + 1) holds, the value ΔE (1+ ) Is set to 0, and ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1 and the node candidate at the time of the exchange is exchanged. The value of one objective function and the value of the original first objective function are exchanged. If the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate
I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of this exchange and the value of the original first objective function are exchanged, and the ΔE (1 -) ≧ 0 and ΔE (1
+) ≧ 0, the node candidates I (j) are not exchanged, the relations ΔE (1-) <0 and ΔE (1 +) <0 hold, and the ΔE (1 If −) is equal to or less than ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) −1, and the value of the first objective function and the element at the time of the exchange are exchanged. The value of the first objective function is exchanged, and ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is greater than ΔE (1+), the node candidate I
(j) is replaced with the node candidate I (j) +1, and the operation of exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange is performed by an odd number. j is performed in ascending order from the smallest to the largest, and even j is performed in the order from the largest to the smallest. If less than or equal to the value obtained by subtracting the threshold value, the operation is performed in the order from small to large for odd j,
And even j are repeated again in ascending order from largest to smallest, and the node candidates are not exchanged at all, or the value of the first objective function is obtained by subtracting a threshold value from the value of the original first objective function. If it is larger, the program to be executed is recorded by terminating the processing.

The one-dimensional time-series data compression program recording medium according to the thirty-ninth aspect of the present invention provides the one-dimensional time-series data compression program recording medium.
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (14), the sub-optimal node candidate calculation is performed by numbering the node candidate index in ascending order of I (j), When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, a node candidate
The value of the first objective function when I (j) is replaced with the node candidate I (j) -1 is calculated, and the value ΔE ( 1−) is calculated, and if the relationship of I (j−1) ≧ I (j) −1 holds, ΔE (1-) is set to 0, and I (j) +
If the relationship 1 <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the first objective function is calculated. Is calculated by subtracting the value of the original first objective function from the value of ΔE (1+), and if the relationship of I (j) + 1 ≧ I (j + 1) holds, then ΔE (1+) Is set to 0, and ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first The value of the objective function is exchanged with the value of the original first objective function. If the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I
(j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1-) ≧ 0 and ΔE (1+)
If the relationship ≧ 0 holds, the node candidates I (j) are not exchanged, the relationship ΔE (1-) <0 and the relationship ΔE (1 +) <0 hold, and the ΔE (1-) Is equal to or less than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function at the time of the replacement and the original first The value of the objective function is exchanged, and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the relationship of ΔE (1-)
Is larger than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) +1, and the value of the first objective function at the time of the replacement and the original The operation of exchanging the value of the first objective function is performed in the order of large to small for the odd j, and in the order of small to large for the even j. If the value of the objective function is less than or equal to the value of the original first objective function minus the threshold, the operation is performed using an odd number
j is repeated from the largest to the smallest, and the even j is repeated again from the smallest to the largest, and whether the node candidates are not exchanged at all or the value of the first objective function is equal to the original first value. If the value is larger than the value obtained by subtracting the threshold value from the value of the objective function, the program for deciding by ending the processing is recorded.

The one-dimensional time-series data compression program recording medium according to claim 40 of the present invention is the recording medium according to claims 28 to 3.
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (14), the sub-optimal node candidate calculation is performed by numbering the node candidate index in ascending order of I (j), When notation 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, node candidates
The value of the first objective function when I (j) is replaced with the node candidate I (j) -1 is calculated, and the value ΔE ((E) is obtained by subtracting the original value of the first objective function from the value of the first objective function. 1−) is calculated, and if the relationship of I (j−1) ≧ I (j) −1 is established, the ΔE (1-) is set to 0, and I (j) +1
If the relationship of <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the first objective function is calculated. A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the value ΔE (1+) is calculated. 0 and the ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first The value of the objective function and the first
The value of the objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j)
Is replaced with the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0
If the relationship holds, the node candidates I (j) are not exchanged, the relationships ΔE (1-) <0 and ΔE (1 +) <0 hold, and the ΔE (1-) If ΔE (1+) or less, the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function at the time of the replacement and the original first
If the values of the objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1-) is greater than the ΔE (1+), An operation of exchanging the node candidate I (j) with the node candidate I (j) +1 and exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange. From j = 1 to [m / 2] and from j = m-1 to [m / 2] +1, and the value of the first objective function at the end of these series of processes is If the value is equal to or less than the value obtained by subtracting the threshold value from the value of one objective function, the above operation is repeated again from j = 1 to [m / 2] and from j = m-1 to [m / 2] +1, and the node candidate If the exchange has not been performed at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the program for making the determination is completed by terminating the process. Record It is obtained by way.

The one-dimensional time-series data compression program recording medium according to claim 41 of the present invention,
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (14), the sub-optimal node candidate calculation is performed by numbering the node candidate index in ascending order of I (j), When notation 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, node candidates
The value of the first objective function when I (j) is replaced with the node candidate I (j) -1 is calculated, and the value ΔE ((E) is obtained by subtracting the original value of the first objective function from the value of the first objective function. 1−) is calculated, and if the relationship of I (j−1) ≧ I (j) −1 is established, the ΔE (1-) is set to 0, and I (j) +1
If the relationship of <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the first objective function is calculated. A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the value ΔE (1+) is calculated. 0 and the ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first The value of the objective function and the first
The value of the objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j)
Is replaced with the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0
If the relationship holds, the node candidates I (j) are not exchanged, the relationships ΔE (1-) <0 and ΔE (1 +) <0 hold, and the ΔE (1-) If ΔE (1+) or less, the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function at the time of the replacement and the original first
If the values of the objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1-) is greater than the ΔE (1+), The operation of exchanging the node candidate I (j) for the node candidate I (j) +1 and exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function is called j. = [M / 2] to 1 and j = [m / 2] +1
To m-1 in order, and if the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is performed by j = [m / 2] to 1 and j = [m / 2] +1 to m−1 again in order, and whether the exchange of node candidates has not been performed at all,
If the value of the first objective function is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the program to be executed is recorded by terminating the processing.

[0050] The one-dimensional time-series data compression program recording medium according to claim 42 of the present invention is characterized by claims 28 to 3.
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (14), the sub-optimal node candidate calculation is performed by numbering the node candidate index in ascending order of I (j), When notation 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, node candidates
The value of the first objective function when I (j) is replaced with the node candidate I (j) -1 is calculated, and the value ΔE ((E) is obtained by subtracting the original value of the first objective function from the value of the first objective function. 1−) is calculated, and if the relationship of I (j−1) ≧ I (j) −1 is established, the ΔE (1-) is set to 0, and I (j) +1
If the relationship of <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the first objective function is calculated. A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the value ΔE (1+) is calculated. 0 and the ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first The value of the objective function and the first
The value of the objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j)
Is replaced with the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0
If the relationship holds, the node candidates I (j) are not exchanged, the relationships ΔE (1-) <0 and ΔE (1 +) <0 hold, and the ΔE (1-) If ΔE (1+) or less, the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function at the time of the replacement and the original first
If the values of the objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1-) is greater than the ΔE (1+), An operation of exchanging the node candidate I (j) with the node candidate I (j) +1 and exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange. Are performed in order from j = 1 to m-1. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the above operation is performed. j = 1 to m-1 again in order, if no exchange of the node candidates has been performed or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value For example, a program to be executed is recorded by terminating the processing.

The one-dimensional time-series data compression program recording medium according to claim 43 of the present invention is characterized in that:
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (14), the sub-optimal node candidate calculation is performed by numbering the node candidate index in ascending order of I (j), When notation 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, node candidates
The value of the first objective function when I (j) is replaced with the node candidate I (j) -1 is calculated, and the value ΔE ((E) is obtained by subtracting the original value of the first objective function from the value of the first objective function. 1−) is calculated, and if the relationship of I (j−1) ≧ I (j) −1 is established, the ΔE (1-) is set to 0, and I (j) +1
If the relationship of <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the first objective function is calculated. A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the value ΔE (1+) is calculated. 0 and the ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first The value of the objective function and the first
The value of the objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j)
Is replaced with the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0
If the relationship holds, the node candidates I (j) are not exchanged, the relationships ΔE (1-) <0 and ΔE (1 +) <0 hold, and the ΔE (1-) If ΔE (1+) or less, the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function at the time of the replacement and the original first
If the values of the objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1-) is greater than the ΔE (1+), An operation of exchanging the node candidate I (j) with the node candidate I (j) +1 and exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange. Are performed in order from j = m-1 to 1. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the above operation is performed. j = m-1 to 1 in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value For example, a program to be executed is recorded by terminating the processing.

The one-dimensional time-series data compression program recording medium according to the forty-fourth aspect of the present invention is the twenty-eighth to thirty-eighth aspect.
1. In the one-dimensional time-series data compression program recording medium according to any one of (1) to (1), when the finally determined number of node candidates is equal to or less than the number of data that was not a candidate, an identifier indicating the node candidate and the final Outputting the compressed data composed of the index number of the node candidate that has been determined and the value of the node candidate, and the finally determined number of node candidates is larger than the number of data that did not become the candidate. In this case, a program for outputting compressed data composed of an identifier that is not a node candidate, an index number of data that has not become a node candidate, and a value of the node candidate is recorded.

The one-dimensional time-series data compression program recording medium according to the forty-fifth aspect of the present invention is the twenty-sixth to the thirty-sixth aspect.
1. The one-dimensional time-series data compression program recording medium according to any one of claims 1 to 3, wherein the recording medium uses the one-dimensional time-series data compression method for time-dependent one-dimensional time-series data A program for independently applying data and compressing each data independently is recorded.

The one-dimensional time-series data compression program recording medium according to the forty-sixth aspect of the present invention is the twenty-sixth to third aspects.
2. The one-dimensional time-series data compression program recording medium according to claim 1, wherein the recording medium compresses the one-dimensional time-series data for each of a plurality of one-dimensional time-series data constituting multi-dimensional time-series data. By repeatedly applying the method, a program for compressing multi-dimensional time-series data is recorded.

The one-dimensional time-series data compression program recording medium according to the forty-seventh aspect of the present invention is the thirty-sixth to third aspects.
1. The one-dimensional time-series data compression program recording medium according to any one of the items 1, wherein the recording medium approximates the one-dimensional time-series data in which a plurality of errors propagate, in order from the one-dimensional time-series data of the propagation source. By increasing the accuracy value and repeatedly applying the one-dimensional time-series data compression method, a program for compressing all the one-dimensional time-series data is recorded.

A one-dimensional time-series data decompression program recording medium according to claim 48 of the present invention uses a program recorded on the one-dimensional time-series data compression program recording medium according to any one of claims 26, 28, and 29. A medium on which a program for expanding compressed compressed data is recorded, wherein the first step of inputting compressed compressed data and the number of data when the compressed data is expanded is the same as the interpolation function used in the compression. A second step of calculating the same number of data as the number of data by interpolating the compressed data using an interpolation function, and calculating a time from the initial time and the time interval by the same number as the number of data; A one-dimensional time-series data decompression program including a third step of outputting the data calculated in the second step and the time is recorded.

A one-dimensional time-series data expansion program recording medium according to claim 49 of the present invention is a program recorded on the one-dimensional time-series data compression program recording medium according to any one of claims 27, 30 and 31. A medium on which a program for expanding compressed compressed data is recorded, wherein a first step of inputting the compressed compressed data and the number of data when the compressed data is expanded is provided. If an identifier indicating that the data is present is given, the time is calculated by the same number as the number of data, and the time is calculated from the initial time and the time interval by the same number as the number of data. If an identifier indicating that is not given, by interpolating the compressed data using the same interpolation function as used in the compression,
A second step of calculating data of the same number as the number of data, and calculating a time from the initial time and the time interval by the same number as the number of data, and the data and the time calculated in the second step; A one-dimensional time series data decompression program including a third step of outputting is recorded.

The one-dimensional time-series data decompression program recording medium according to claim 50 of the present invention is the recording medium of claim 48 or 4.
9. In the one-dimensional time-series data decompression program recording medium according to 9, the program recorded on the medium is used for each of a plurality of compressed one-dimensional time-series data constituting the compressed multi-dimensional time-series data. By repeatedly applying the one-dimensional time-series data expansion method, a program for expanding the compressed multi-dimensional time-series data is recorded.

A one-dimensional time-series data compression device according to claim 51 of the present invention is a device for compressing one-dimensional time-series data at equal time intervals, and inputs the one-dimensional time-series data and its approximation accuracy. First means, second means for calculating a candidate node of an interpolation function that approximates the one-dimensional time-series data, third means for optimizing the position of the candidate node,
Fourth means for determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data based on the node candidates whose positions have been optimized; and When it is determined that the value exceeds the value based on the approximation accuracy, the number of nodes is changed, and the fifth means returns to the second means. A sixth means for outputting the data of the node candidate and the data of the time corresponding to the node candidate as compressed information when it is determined that the node candidate is not exceeded is provided.

A one-dimensional time-series data compression apparatus according to claim 52 of the present invention is a one-dimensional time-series data compression apparatus for compressing one-dimensional time-series data at equal time intervals, and inputs the one-dimensional time-series data and its approximation accuracy. First means, second means for determining whether or not data within the approximation accuracy is included in the one-dimensional time-series data, and the first means
Third means for calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data when it is determined that the data within the approximation accuracy is not included in the one-dimensional time-series data;
Fourth means for optimizing the position of the node candidate, and determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data based on the node candidate having the optimized position. A sixth means for changing the number of nodes when it is determined by the fifth means that the error exceeds a value based on the approximation accuracy, and returning to the third means.
Means, and when it is determined by the second means that the one-dimensional time-series data includes data within the approximation accuracy, the one-dimensional time-series data is data within the approximation accuracy. Outputting information, and when the fifth means determines that the error does not exceed the value based on the approximation accuracy, outputs the data of the node candidate and the data of the time corresponding thereto as compressed information. And a seventh means for performing the operation.

The one-dimensional time-series data compression apparatus according to claim 53 of the present invention is a means for compressing one-dimensional time-series data at equal time intervals, and inputs the one-dimensional time-series data and its approximation accuracy. First means for adding an index to the one-dimensional time-series data in the order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; From inside, always include the beginning and end data, and second means for randomly determining only a few node candidates of the nodes, and interpolating the node candidates by an interpolation function using an index number as an independent variable, Third means for calculating an error from the original one-dimensional time-series data, and calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance Do Means 4 performs the value of the first objective function repeats the change of the node candidates so as to minimize,
Fifth means for determining a sub-optimal node candidate, and generating one-dimensional time-series data approximating the original one-dimensional time-series data by interpolating the sub-optimal node candidate using the interpolation function.
Sixth means for calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data, and a second object defined by weighted addition of the maximum value of the error, the error average and the error variance from the error Seventh means for calculating a value of the function, and if the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy,
A value obtained by adding an increment to the number of nodes is set as a new number of nodes, and the process from the second means to the seventh means is repeated.
Means, and if the value of the second objective function is less than the threshold, an initial time and a time interval of the one-dimensional time-series data;
A ninth output unit outputs compressed data including the finally determined index number of the node candidate and the value of the node candidate.
Means are provided.

A one-dimensional time-series data compression apparatus according to claim 54 of the present invention is a one-dimensional time-series data compression apparatus for compressing one-dimensional time-series data at equal time intervals, and inputs the one-dimensional time-series data and its approximation accuracy. First means for adding an index to the one-dimensional time-series data in the order of time and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; Second means for always including the start and end data and determining only a few node candidates so as to be approximately equally spaced with respect to the index, and independent index numbers for the node candidates Third means for calculating an error from the original one-dimensional time-series data by interpolating using an interpolation function as a variable, and weighting the maximum value of the error, the error average, and the error variance from the error. A fourth means for calculating the value of the first objective function defined in the above, and a fifth means for repeatedly changing the node candidates so as to minimize the value of the first objective function and determining the sub-optimal node candidates Means for interpolating the sub-optimal node candidates using the interpolation function to generate one-dimensional time-series data approximating the original one-dimensional time-series data; A sixth means for calculating an error of the second objective function from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error and the error variance; If the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy, a value obtained by adding an increment to the number of nodes is set as a new number of nodes, and
Eighth means for repeating the processing from the means to the seventh means, and if the value of the second objective function is less than the threshold value, the initial time and time interval of the one-dimensional time-series data are finally determined. Ninth means for outputting compressed data composed of the index numbers of the selected node candidates and the values of the node candidates.

A one-dimensional time-series data compression device according to claim 55 of the present invention is a device for compressing one-dimensional time-series data at equal time intervals, and inputs said one-dimensional time-series data and its approximation accuracy. First means for adding an index to the one-dimensional time-series data in order of time, calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data, and an absolute value of the one-dimensional time-series data Is determined to be less than or equal to the approximation accuracy. If the accuracy is less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output and the process is terminated. If not, the process proceeds to a third means described later. Second means, third means for always including the start and end data from the one-dimensional time-series data, and randomly determining only a few node candidates, and indexing the node candidates Number Fourth means for calculating an error from the original one-dimensional time-series data by interpolating using an interpolation function as a vertical variable, and weighting addition of the maximum value of the error, the error average, and the error variance from the error. Fifth means for calculating the value of the defined first objective function, and sixth means for repeatedly changing the node candidates so as to minimize the value of the first objective function and determining the sub-optimal node candidates And interpolating the sub-optimal node candidates by the interpolation function to generate one-dimensional time-series data approximating the original one-dimensional time-series data, and combining the one-dimensional time-series data with the original one-dimensional time-series data A seventh means for calculating an error, an eighth means for calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance; (2) a threshold value of the objective function corresponding to the approximation accuracy If above, then the new number of nodes not containing added increment the number of nodes, the third
Ninth means for repeating the processing from the means to the eighth means, and if the value of the second objective function is less than the threshold value, the initial time and time interval of the one-dimensional time-series data are finally determined. And a tenth means for outputting compressed data composed of the index numbers of the selected node candidates and the values of the node candidates.

A one-dimensional time-series data compression apparatus according to claim 56 of the present invention is a one-dimensional time-series data compression apparatus for compressing one-dimensional time-series data at equal time intervals, and inputs the one-dimensional time-series data and its approximation accuracy. First means for adding an index to the one-dimensional time-series data in order of time, calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data, and an absolute value of the one-dimensional time-series data It is determined whether or not all are less than or equal to the approximation accuracy. If the is less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output, and if not, the process proceeds to a third means described later. A third means for determining node candidates of only a few nodes from the one-dimensional time-series data so as to always include start and end data and to be approximately equally spaced with respect to the index. Means of A fourth means for interpolating the node candidate by an interpolation function using an index number as an independent variable to calculate an error from the original one-dimensional time-series data; Means for calculating a value of a first objective function defined by weighting addition of error and error variance, and repeatedly changing a node candidate so as to minimize the value of the first objective function, Sixth means for determining a candidate, and interpolating the sub-optimal node candidate using the interpolation function to generate one-dimensional time-series data approximating the original one-dimensional time-series data. Seventh means for calculating an error from the original one-dimensional time-series data, and calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance Eighth means for performing If the value of the objective function is equal to or greater than the threshold value corresponding to the approximation accuracy, a value obtained by adding an increment to the number of nodes is set as a new number of nodes, and the ninth and eighth processes of repeating the processes from the third means to the eighth means are repeated. Means, if the value of the second objective function is less than the threshold, the initial time and time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate And a tenth means for outputting the configured compressed data.

According to a one-dimensional time-series data compression apparatus according to claim 57 of the present invention, in the one-dimensional time-series data compression apparatus according to any one of claims 52 to 56, the suboptimal node candidate calculation is performed by The index of the node candidate index is assigned
(j), if 0 ≤ j ≤ m, the node candidate I (j) is replaced with the node candidate I (j) -1 if the relationship I (j-1) <I (j) -1 holds. The value of the first objective function at the time of
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1) is calculated, and if I (j-1) ≧ I (j) -1, the ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is obtained. Holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Calculate the value ΔE (1+) by subtracting the function value,
If I (j) + 1 ≧ I (j + 1), the ΔE (1+) is set to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, The node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j ) Is replaced with the node candidate I (j) +1,
If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE
(1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I
(j) is replaced with the node candidate I (j) -1, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and the ΔE (1-)
Is larger than the ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 is performed in the order of odd to j from small to large, and even j Are performed in the order from the largest to the smallest, and if the value of the first objective function at the end of the series of processes is equal to or less than the value obtained by subtracting the threshold from the value of the original first objective function, the operation is performed in an odd number. J is performed again in ascending order from the smallest to the largest j, and for even j, the order is changed from the largest to the smallest, and whether the node candidates have not been exchanged at all or the value of the first objective function is If the value is larger than the value obtained by subtracting the threshold value from the value of one objective function, the processing is terminated to end the processing.

A one-dimensional time-series data compression apparatus according to claim 58 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 53 to 56, wherein the suboptimal node candidate calculation is The index of the node candidate index is assigned
(j), if 0 ≤ j ≤ m, the node candidate I (j) is replaced with the node candidate I (j) -1 if the relationship I (j-1) <I (j) -1 holds. The value of the first objective function at the time of
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + If the relationship of 1) holds, the node candidate I (j) is replaced by the node candidate I (j) +1
The value of the first objective function at the time of replacement is calculated, a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) If the relationship of + 1 ≧ I (j + 1) holds, set ΔE (1+) to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, Node candidate
I (j) is replaced with the node candidate I (j) -1, and ΔE (1-) ≧ 0
And if the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the ΔE (1-) ≧
0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidates I (j) are not exchanged, and the relationships of ΔE (1-) <0 and ΔE (1 +) <0 hold. And, if the ΔE (1-) is not more than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and ΔE (1 +) <0
Holds, and ΔE (1-) is greater than ΔE
If it is larger than (1+), the operation of exchanging the node candidate I (j) with the node candidate I (j) +1 is performed in the order from the largest to the smallest for the odd j, and smaller for the even j. If the value of the first objective function at the end of the series of processes is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the above operation is performed for odd j. The order from the largest to the smallest one and the j of the even number are repeated again from the smallest to the largest one, and the exchange of the node candidates was not performed at all, or the value of the first objective function was changed to the value of the original first objective function. If the value is larger than the value obtained by subtracting the threshold value from the value, the processing is terminated to end the processing.

The one-dimensional time-series data compression apparatus according to claim 59 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 53 to 56, wherein the suboptimal node candidate calculation is performed by The index of the node candidate index is assigned
(j), when 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, replace the node candidate I (j) with the node candidate I (j) -1 The value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function
If the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is established. Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Is calculated by subtracting the value of ΔE (1 +). If the relationship of I (j) + 1 ≧ I (j + 1) holds,
(1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) ≧ 0 and the ΔE
If the relationship of (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 If the relationship holds, the node candidate I (j)
Are not exchanged, the ΔE (1-) <0 and the ΔE (1 +) <0
Holds, and the ΔE (1-) is the ΔE (1+)
If below, the node candidate I (j) is replaced with the node candidate I (j) -1, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and If ΔE (1-) is larger than ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 is performed from j = 1 to [m / 2]. And j = m-1 to [m / 2] +1, and the value of the first objective function at the end of the series of processes is obtained by subtracting the threshold from the value of the original first objective function. If the following, the above operation is performed again from j = 1 to [m / 2] and from j = m-1 to [m / 2] +1 again, and whether or not the exchange of the node candidates has been performed at all, If the value of the first objective function is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the processing is terminated to terminate the processing.

A one-dimensional time-series data compression apparatus according to claim 60 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 53 to 56, wherein the suboptimal node candidate calculation is The index of the node candidate index is assigned
(j), if 0 ≤ j ≤ m, the node candidate I (j) is replaced with the node candidate I (j) -1 if the relationship I (j-1) <I (j) -1 holds. The value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function
If the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is established. Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Is calculated by subtracting the value of ΔE (1 +). If the relationship of I (j) + 1 ≧ I (j + 1) holds,
(1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) ≧ 0 and the ΔE
If the relationship of (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 If the relationship holds, the node candidate I (j)
Are not exchanged, the ΔE (1-) <0 and the ΔE (1 +) <0
Holds, and if ΔE (1-) is equal to or smaller than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j). The operation to exchange for +1 is from j = [m / 2] to 1 and from j = [m / 2] +1
m−1, and if the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is performed by j = [m / 2] to 1 and j = [m / 2] +1 to m-1 again, and whether the exchange of the node candidates has not been performed at all,
If the value of the first objective function is greater than the value of the original first objective function minus a threshold value, the processing is terminated to terminate the processing.

The one-dimensional time-series data compression device according to claim 61 of the present invention is the one-dimensional time-series data compression device according to any one of claims 53 to 56, wherein the calculation of the sub-optimal node candidate is performed by The index of the node candidate index, which is numbered in ascending order, is
(j), if 0 ≤ j ≤ m, the node candidate I (j) is replaced with the node candidate I (j) -1 if the relationship I (j-1) <I (j) -1 holds. The value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function
If the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is established. Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Is calculated by subtracting the value of ΔE (1 +). If the relationship of I (j) + 1 ≧ I (j + 1) holds,
(1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) ≧ 0 and the ΔE
If the relationship of (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 If the relationship holds, the node candidate I (j)
Are not exchanged, the ΔE (1-) <0 and the ΔE (1 +) <0
Holds, and if ΔE (1-) is equal to or smaller than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j). The operation of exchanging for +1 is performed in order from j = 1 to m−1, and the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function. Then, j =
1 to m-1 again in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is greater than the value of the original first objective function minus a threshold, The processing is performed by terminating the processing.

The one-dimensional time-series data compression apparatus according to claim 62 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 53 to 56, wherein the calculation of the sub-optimal node candidate is performed by using the node Candidate indexes are numbered in ascending order as I (j),
When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. 1) calculate the value of the objective function, calculate a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, and obtain I (j-1) ≧ I (j) − If the relationship of 1 holds, the above ΔE (1
-) Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first node when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1 ), The above-mentioned ΔE (1
+) Is set to 0, ΔE (1-) <0 and ΔE (1+) ≧ 0
If the relationship holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) ≧ 0 and the ΔE (1
+) <0, the node candidate I (j) is replaced with the node candidate I (j) +1, and ΔE (1-) ≧ 0 and Δ
If the relationship of E (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and If ΔE (1-) is equal to or smaller than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and ΔE (1-) <0 and ΔE (1 +) <0, and if ΔE (1-) is greater than ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 is performed. j = m-1 to 1 in order, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operation is performed by j =
m-1 to 1 in order, and if no exchange of the node candidates has been performed, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold, The processing is performed by terminating the processing.

The one-dimensional time-series data compression device according to claim 63 of the present invention is the one-dimensional time-series data compression device according to any one of claims 53 to 56, wherein the calculation of the sub-optimal node candidate is performed by The index of the node candidate index is assigned
(j), when 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, replace the node candidate I (j) with the node candidate I (j) -1 The value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function
If the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is established. Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Is calculated by subtracting the value of ΔE (1 +). If the relationship of I (j) + 1 ≧ I (j + 1) holds,
(1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship of ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of this exchange and the original first objective function Are exchanged, and if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is replaced with the node candidate I (j) +1.
And the value of the first objective function at the time of this exchange is exchanged with the value of the original first objective function, so that ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 If the relationship holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1 and the value of the first objective function when the exchange is performed is The value of the original first objective function is exchanged, and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is the ΔE (1+) If it is larger, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original first objective function The operation of exchanging values is performed in the order of small to large for odd j,
And even j are performed in order from the largest to the smallest, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, The operation is performed again in the order of small to large for the odd j, and in the order of large to small for the even j. If the value is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, the processing is terminated to end the processing.

A one-dimensional time-series data compression apparatus according to a sixty-fourth aspect of the present invention is the one-dimensional time-series data compression apparatus according to any one of the fifty-third to fifty-sixth aspects, wherein the suboptimal node candidate calculation is Candidate indexes are numbered in ascending order as I (j),
When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. 1) calculate the value of the objective function, calculate a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, and obtain I (j-1) ≧ I (j) − If the relationship of 1 holds, the above ΔE (1
-) Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first node when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1 ), The above-mentioned ΔE (1
+) Is set to 0, ΔE (1-) <0 and ΔE (1+) ≧ 0
Is satisfied, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first candidate at the time of the exchange is
The value of the objective function and the value of the original first objective function are exchanged, and if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is determined. The node candidate is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1
-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 is satisfied. The relationship holds, and the ΔE (1-)
Is less than or equal to ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function at the time of the replacement and the original first If the values of the objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1-) is greater than the ΔE (1+), An operation of exchanging the node candidate I (j) with the node candidate I (j) +1 and exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange. The odd j
Are performed in ascending order from largest to smallest, and even j is performed in ascending order from smallest to largest. When the series of processes is completed, the value of the first objective function is determined as a threshold from the value of the original first objective function. If it is less than or equal to, the above operation is performed again in the order of large to small for odd j, and in the order of small to large for even j, and whether the exchange of node candidates has not been performed at all, If the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is terminated to make a decision.

A one-dimensional time-series data compression apparatus according to a sixty-fifth aspect of the present invention is the one-dimensional time-series data compression apparatus according to any one of the fifty-third to fifty-sixth aspects, wherein the calculation of the suboptimal node candidate is performed by Candidate indexes are numbered in ascending order as I (j),
When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. 1) calculate the value of the objective function, calculate the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, and obtain I (j-1) ≧ I (j) − If the relationship of 1 holds, the above ΔE (1
-) Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first node when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1 ), The above-mentioned ΔE (1
+) Is set to 0, ΔE (1-) <0 and ΔE (1+) ≧ 0
Is satisfied, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first candidate at the time of the exchange is
The value of the objective function and the value of the original first objective function are exchanged, and if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is determined. The node candidate is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1
-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 is satisfied. The relationship holds, and the ΔE (1-)
Is equal to or less than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function at the time of the replacement and the original first If the values of the objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1-) is greater than the ΔE (1+), An operation of exchanging the node candidate I (j) with the node candidate I (j) +1 and exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange. From j = 1 to [m / 2] and from j = m-1 to [m / 2] +1, and the value of the first objective function at the end of these series of processes is the original If the value is equal to or less than the value obtained by subtracting the threshold from the value of one objective function, the operation is performed from j = 1 to [m / 2] and j =
m-1 to [m / 2] +1, and the exchange of the node candidates was not performed at all, or the value of the first objective function was obtained by subtracting a threshold value from the value of the original first objective function. If it is larger than the value, the decision is made by terminating the process.

A one-dimensional time-series data compression apparatus according to claim 66 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 53 to 56, wherein the calculation of the sub-optimal node candidate is performed by Candidate indexes are numbered in ascending order as I (j),
When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. 1) calculate the value of the objective function, calculate the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, and obtain I (j-1) ≧ I (j) − If the relationship of 1 holds, the above ΔE (1
-) Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first node when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1 ), The above-mentioned ΔE (1
+) Is set to 0, ΔE (1-) <0 and ΔE (1+) ≧ 0
Is satisfied, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first candidate at the time of the exchange is
The value of the objective function and the value of the original first objective function are exchanged, and if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is determined. The node candidate is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1
-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 is satisfied. The relationship holds, and the ΔE (1-)
Is less than or equal to ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function and the original first If the values of the objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1-) is greater than the ΔE (1+), The operation of exchanging the node candidate I (j) for the node candidate I (j) +1 and exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function is called j. = [M / 2] to 1 and j = [m / 2] +1 to m-1 in order, and the value of the first objective function when these series of processes are completed is the original first objective. If the value is equal to or less than the value of the function minus the threshold, the operation is performed from j = [m / 2] to 1 and j =
[M / 2] +1 to m-1 in order, and the exchange of the node candidates was not performed at all, or the value of the first objective function was obtained by subtracting a threshold value from the value of the original first objective function. If the value is larger than the value, the process is terminated to terminate the process.

The one-dimensional time-series data compression apparatus according to claim 67 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 53 to 56, wherein the calculation of the sub-optimal node candidate is performed by Candidate indexes are numbered in ascending order as I (j),
When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. 1) calculate the value of the objective function, calculate the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, and obtain I (j-1) ≧ I (j) − If the relationship of 1 holds, the above ΔE (1
-) Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first node when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1 ), The above-mentioned ΔE (1
+) Is set to 0, ΔE (1-) <0 and ΔE (1+) ≧ 0
Is satisfied, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first candidate at the time of the exchange is
The value of the objective function and the value of the original first objective function are exchanged, and if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is determined. The node candidate is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1
-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 is satisfied. The relationship holds, and the ΔE (1-)
Is equal to or less than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function at the time of the replacement and the original first If the values of the objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1-) is greater than the ΔE (1+), An operation of exchanging the node candidate I (j) with the node candidate I (j) +1 and exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange. From j = 1
m-1 in order, and if the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the above operation is performed from j = 1 to m. -1 until the node candidates have not been exchanged at all, or if the value of the first objective function is greater than the value of the original first objective function minus a threshold value, the process is terminated. By doing so, it is done.

The one-dimensional time-series data compression apparatus according to claim 68 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 53 to 56, wherein the calculation of the sub-optimal node candidate is performed by Candidate indexes are numbered in ascending order as I (j),
When 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j) -1. 1) calculate the value of the objective function, calculate the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, and obtain I (j-1) ≧ I (j) − If the relationship of 1 holds, the above ΔE (1
-) Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first node when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the objective function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1 ), The above-mentioned ΔE (1
+) Is set to 0, ΔE (1-) <0 and ΔE (1+) ≧ 0
Is satisfied, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the first candidate at the time of the exchange is
The value of the objective function and the value of the original first objective function are exchanged, and if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is determined. The node candidate is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1
-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 is satisfied. The relationship holds, and the ΔE (1-)
Is less than or equal to ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the value of the first objective function at the time of the replacement and the original first If the values of the objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1-) is greater than the ΔE (1+), An operation of exchanging the node candidate I (j) with the node candidate I (j) +1 and exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange. Is performed in order from j = m-1 to 1. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the above operation is performed. j = m-1 to 1 in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value Ba By terminating the process, in which to carry out.

A one-dimensional time-series data compression apparatus according to claim 69 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 53 to 56, wherein the finally determined number of node candidates is If not more than the number of data that was not a candidate, output compressed data consisting of an identifier indicating the node candidate, the index number of the finally determined node candidate and the value of the node candidate, If the finally determined number of node candidates is larger than the number of data that did not become the candidate, it is composed of an identifier that is not a node candidate, the index number of the data that did not become the node candidate, and the value of the node candidate. The compressed data thus output is output.

A one-dimensional time-series data compression apparatus according to claim 70 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 51 to 56, wherein the one-dimensional time-series data compression apparatus is unequally spaced with respect to time. For data,
The dimensional time-series data compression device is applied independently for time and data, and each is compressed independently.

A one-dimensional time-series data compression apparatus according to a seventy-first aspect of the present invention is the one-dimensional time-series data compression apparatus according to any one of the fifty-first to fifty-sixth aspects, By repeatedly applying the one-dimensional time-series data compression device to each of the one-dimensional time-series data, the multi-dimensional time-series data is compressed.

A one-dimensional time-series data compression apparatus according to claim 72 of the present invention is the one-dimensional time-series data compression apparatus according to any one of claims 51 to 56, wherein the one-dimensional time-series data compression apparatus transmits a plurality of errors. All the one-dimensional time-series data is compressed by increasing the approximation accuracy value for the data in order from the one-dimensional time-series data of the propagation source and repeatedly applying the one-dimensional time-series data compression device. It is like that.

A one-dimensional time-series data decompression device according to claim 73 of the present invention is a device for decompressing the compressed data compressed by the one-dimensional time-series data compression device according to any one of claims 51, 53 and 54. The first means for inputting the compressed data and the number of data when the compressed data is decompressed, and interpolating the compressed data using the same interpolation function as the interpolation function used for compression. A second means for calculating the same number of data as the number of data, and calculating a time from the initial time and the time interval by the same number as the number of data; and the data and the time calculated by the second means. And a third means for outputting the same.

A one-dimensional time-series data decompressing apparatus according to claim 74 of the present invention expands the compressed data compressed by the one-dimensional time-series data compressing apparatus according to any one of claims 52, 55 and 56. And first means for inputting the compressed data and the number of data when the data is decompressed, and when the compressed data is provided with an identifier indicating that the data is all 0, When the time is calculated by the same number as the number of data and the initial time and the time interval from the same number of 0s as the number of the data, and if the identifier indicating that all the data is 0 is not given to the compressed data, By interpolating the compressed data using the same interpolation function as that used for compression, the same number of data as the number of data is calculated, and the time is calculated from the initial time and the time interval as the number of data. Minute Only the second means for calculating, in which as and a third means for outputting the said data and the time calculated by the second means.

A one-dimensional time-series data decompressing apparatus according to claim 75 of the present invention is the one-dimensional time-series data decompressing apparatus according to claim 73 or 74, wherein a plurality of compression units forming the compressed multi-dimensional time-series data are provided. The compressed one-dimensional time-series data is expanded by repeatedly applying the one-dimensional time-series data decompression device to each of the one-dimensional time-series data.

[0084]

BEST MODE FOR CARRYING OUT THE INVENTION

Embodiment 1 FIG. Hereinafter, the one-dimensional time-series data compression method according to the first embodiment of the present invention will be described with reference to the drawings. FIG. 1 shows a processing flow of the one-dimensional time-series data compression method according to the first embodiment of the present invention.

In the figure, P4a is an input process for inputting one-dimensional time-series data and its approximation accuracy value, and P1a is a node candidate calculation for calculating a candidate for a node through which an interpolation function approximating the one-dimensional time-series data passes. Process P1b is a node position optimization process for optimizing the position of the node candidate calculated by the node candidate calculation process P1a, and P1c is an interpolation function passing through the node obtained by the node position optimization process P1b and the original 1 A determination process of determining whether an error from the dimensional time-series data satisfies a value corresponding to the approximation accuracy value input in the input process P4a. P1d determines that the approximation accuracy is not satisfied in the determination process P1c. In this case, the number of nodes is changed, and the number of nodes is changed. P4b determines the error between the interpolation function passing through the nodes and the original one-dimensional time-series data by the determination process P1c. In an output process of outputting the node and the index as compressed information if they satisfy the values corresponding to the approximation accuracy value input.

The method for compressing one-dimensional time-series data according to the first embodiment uses an interpolation function to generate a smaller number of nodes than the number of data of given one-dimensional time-series data, thereby compressing the data. It is intended to realize. That is, data compression is performed by calculating a node of an interpolation function necessary to reproduce data approximated to the original one-dimensional time-series data and transmitting the data excluding the node. . Then, the decompression approximates the transmitted data to the original time-series data by generating the same data as the data omitted at the time of compression using the same interpolation function as the interpolation function used at the time of compression. This is performed by generating time-series data.

More specifically, as shown in FIG. 1, in an input process P4a, one-dimensional time-series data to be compressed and its approximate accuracy value are input, and in the node candidate calculation process P1a, the one-dimensional time-series data is formed. A node candidate is calculated from all the one-dimensional data to be generated, and a predetermined interpolation function passes through the node data to generate a one-dimensional time-series data approximating the original one-dimensional time-series data. In the node position optimization process P1b, the node candidate is moved to optimize the node position, and the determination process P
In 1c, it is determined whether or not a value based on an error between a predetermined interpolation curve passing through the optimized node candidate and the original one-dimensional time-series data is within a range of the approximation accuracy value input in the input processing P4a. If it is within the range of the approximation accuracy, the node candidate whose node position has been optimized by the output process P4b and its index are output as compressed one-dimensional time-series data.

If it is determined in the determination process P1c that the value does not fall within the range of the approximation accuracy, the number of nodes is changed by appropriately increasing or decreasing the number of nodes in the number-of-nodes changing process P1d. After the nodes are changed by the node number changing process P1d, the process returns to the node candidate calculating means P1a to calculate the node candidates again, and thereafter, the same process is repeated.

As described above, the data compression method shown in FIG. 1 uses the interpolation function to generate a smaller number of nodes than the number of given one-dimensional time-series data, thereby compressing the data. Since it is intended to be realized, if a discrete Fourier series expansion or a discrete cosine series expansion is used as an interpolation function, the positions for obtaining these coefficients can be reliably reduced from the original time-series data. In addition, since the nodes are optimized not only for their positions but also for the number,
An error between the decompressed data and the original data is small, and compression with a good compression ratio is possible. Also, by specifying a large error range that occurs during expansion during compression, it is possible to further reduce the number of nodes.
Data compression with a better compression ratio can be realized.

However, these are determined depending on the reproduction accuracy when the data is expanded. Further, since the data compression ratio depends on how the original time-series data can be approximated within the range of the accuracy of the designated error, the data compression ratio is generally not constant. Further, if the data of high-frequency components is cut as in the related art, it is possible to further increase the compression ratio as compared with the related art. That is, when used in combination with the conventional technology, it can be used as a complementary method for further increasing the compression ratio in the conventional technology.

Of course, even if the data is compressed only by the compression method of the first embodiment without cutting the high-frequency component, the number of selected nodes is the same as the frequency component remaining after the high-frequency component is cut by the conventional compression method. If the number is smaller than the number, the compression ratio of the present invention is higher. However, since it is determined depending on the properties of the given one-dimensional time-series data, it cannot be generally determined that either method has a high compression ratio. However, according to the present invention, the range of choice of the data compression method is expanded.

Further, a polynomial expression as an interpolation function,
For example, when a spline function or the like is used, the data when expanded is data that undergoes a polynomial change. This is effective in maintaining the accuracy when one-dimensional time-series data having no periodicity is expanded. Therefore, even if the number of data to be decompressed is made different from the number of the original data, the accuracy can be maintained even if the decompression is performed.If the data generated at the time of decompression is reduced, the original data can be reproduced at high speed, Even if high-speed reproduction is performed, the accuracy of the data can be maintained. Conversely, if the data generated at the time of decompression is increased, the original data can be reproduced at a slow speed, and the accuracy of the data can be maintained even when the data is reproduced at a slow speed.

As described above, Embodiment 1 not only complements the conventional compression method but also provides a new compression method for performing compression suited to the properties of one-dimensional time-series data. It is possible to expand the range of choices.

Hereinafter, the processing of the first embodiment of the present invention will be described in more detail. Before that, one-dimensional time-series data will be described with reference to FIG. FIG. 12 is a graph of one-dimensional time-series data, in which black circles represent one-dimensional data. In this way, the one-dimensional data and the time corresponding thereto are paired data as 1
It is called dimensional time series data. Then, when the time at which the data is sampled is represented as t0,..., Tn as shown in FIG. The case is called an equal time interval, and the other case is called an irregular time interval.

FIG. 2 shows a processing flow of the one-dimensional time-series data compression method according to the first embodiment of the present invention. As shown in FIG. 2, the entire process is executed in nine stages from a first stage S1 to a ninth stage S9. The first stage S1 includes processes P1 to P3, the second stage S2 includes process P4, and the third stage S3 includes process P5.
The fourth stage S4 comprises a process P7, the fifth stage S5 comprises a process P8, the sixth stage S6 comprises a process P9 and a process P10, and a seventh stage S6.
7 comprises a process P11, an eighth stage S8 comprises processes P4 to P13, and a ninth stage S9 comprises a process P1.
4.

FIG. 3 shows an example of the configuration of a computer for performing the flow processing of FIG. 1 in which the detailed processing is shown in FIG. 2. In FIG. 2 is a data memory for storing data to be processed by the CPU 1, 3 is a main memory for storing in advance a control program corresponding to the processing of FIG. An input / output device 5 for inputting and outputting data is a bus through which the CPU 1, data memory 2, main memory 3 and input / output device 4 exchange data and the like with each other. Note that the data memory 2 and the main memory 3 may be configured using the same memory. The CPU 1 executes a compression process shown as a flow in FIG. 2 according to a control program stored in the main memory 3 in advance.

FIG. 3B shows an example of the configuration of a computer which reads a program from a program recording medium or the like to perform a compression operation. In FIG. 3B, reference numeral 6 denotes an external storage connected to the bus 5 A control program corresponding to the processing of FIG. 2 is recorded in advance on a recording medium of the external storage device, and the external storage device 6 reads the control program corresponding to the processing of FIG. 2 from the recording medium. , Is loaded into the main memory 3. The CPU 1 executes the compression processing shown in the flow of FIG. 2 according to the control program loaded in the main memory 3. Alternatively, a control program supplied from the outside via the input / output device 4 may be loaded into the main memory 3.

Next, the first of FIG.
Steps S1 to S9 will be described. First,
In process P1, one-dimensional time-series data to be data-compressed and an approximation accuracy value of an interpolation function that approximates the data are input. In process P2, the one-dimensional time-series data is indexed in the order of the time. As this time, a sample time, an occurrence time, an input time, or the like of the one-dimensional time-series data can be used. It should be noted that the index may use data that increases sequentially or data that decreases sequentially instead of the time. In process P3, the initial number of nodes is calculated. Since the initial value of the number of nodes used at that time is determined according to the type of the interpolation function, the initial value may be set in advance. Therefore, for example, the ratio to the initial number of data is determined in advance. Thus, this can be calculated. Here, it is assumed that the initial number of nodes is calculated in the form of 1 / a of the total number of one-dimensional time series data (where a> 0) as an initial value of the number of nodes to be used.

In the process P4, one-dimensional time-series data to be data-compressed must always include the beginning and end data, and the remaining data is selected at random intervals. The node candidates are determined so as to have the same number as the calculated number of nodes.

This operation will be described with reference to FIG. now,
Assuming that the number of nodes is m + 1, the data at time t0 is the first data, and this is selected as the first node candidate. Next, the data at time tn is the end data,
This is selected as the last node candidate. Next, 1 / (n-1)
The remaining m-1 node candidates are selected without overlapping each other by random numbers generated with the uniform probability of. After a total of m + 1 node candidates have been selected in this way, they are sorted in ascending order of time, and the index of the node candidates is set to I (j),
Store as 0 ≤ j ≤ m. In the example of FIG. 13, data indicated by white circles is selected as a node candidate.

Although the above is the case of random selection, the processing P4 for obtaining the node candidates may be selected at approximately equal intervals with respect to the index. In this case, first, an interval [n / m] is calculated with respect to the index, and a total of m node candidates separated by this interval [n / m] starting from the first data at time t0 are selected, and the (m + 1) th node is selected. Time as a candidate
End by selecting the ending data at tn. Here, [x] is a Gaussian symbol. Again,
I (j) as described above is stored.

The operation performed in the process P4 is to determine the initial value of the position of the node candidate, and it is known that it is effective to use a random number for this kind of problem. Even in the case of, a better value is experimentally obtained when the node positions are selected using random numbers than when the node positions are selected at approximately equal intervals.

In process P5, data for interpolating between the node candidates is generated by an interpolation function using the index number as an independent variable, and one-dimensional time-series data approximating the original one-dimensional time-series data is obtained. And the original one-dimensional time-series data are calculated. The interpolation function may be anything as long as it passes through a node. For example, a spline function has a property that can be used as an interpolation function passing through a node. However, if the decompressed data should reproduce a waveform that is faithful to the waveform of the original data, it is desirable to use an interpolation function that can faithfully approximate the original one-dimensional time-series data. If a rate is required, the interpolation function does not require much closeness. In addition, a series expansion expression using a discrete Fourier transform, a series expansion expression using a discrete cosine transform, or the like can also be used as an interpolation function. However, any one of the above-mentioned interpolation functions is selected in advance and used. Then, the same interpolation function as that used for compression in the case of decompression processing to be described later is used. In this case, a plurality of candidates for the interpolation function are prepared in advance, the identifier of the interpolation function used at the time of compression is sent to the decompression processing side, and the same interpolation function as at the time of compression is used on the decompression side. Is also good.

FIG. 14 is a graph of an interpolation function for interpolating the curve of FIG. The black circles in the figure are data obtained by interpolating node candidates represented by white circles using an interpolation function, and these are rejected during data compression. Most of the data indicated by the black circles has the same value as the original data, but an error has occurred in the data at time tn-1. In the process P6, as shown in FIG.
An error between the one-dimensional time-series data other than the node candidates and the interpolation function is calculated. In the case of FIG. 14, the calculation of the error is performed using the absolute value error, but the calculation of the error may be performed using a square error or the like. In process P7, the value of the first objective function is calculated from the error calculated in process P6. This first objective function can be calculated by first obtaining the maximum value, error average, and error variance of the error calculated in the process P6, and weighting and adding them.

This objective function is, in other words, an error evaluation function. The maximum value of the error between the one-dimensional time series data generated from the selected node candidate and the original one-dimensional time series data, the average of the errors, and the error are used. From the viewpoint that the one with both small variances is the best node candidate, the value obtained by weighting and adding the maximum value of the error, the average of the error, and the variance of the error is evaluated so that the error is evaluated. This is used as an error evaluation function.

The weighting coefficient includes a method in which the value is fixed from the beginning and a method in which the value is variably determined according to data. In the case of variably determining, for example, when it is desired to equally allocate the weights for the maximum error, error average, and error variance, the product of each weight and their value may be determined to be equal. When it is determined from the beginning, for example, the values of the weighting factors are all determined to be ““ ”in advance. In general, actual data is often processed several times to determine a value that is considered empirically good.

In the process P8, the node candidates are repeatedly changed so as to minimize the value of the first objective function, and the sub-optimal node candidates are determined. This is the same as the first method shown in FIG. There are two methods of the second method shown in FIG.

The process of determining the sub-optimal node candidate is performed by obtaining the value of the objective function when a certain node candidate is determined and the value of the objective function when the node candidate is changed, and calculating the difference between these values. By selecting a node candidate such that the difference becomes small, a local optimum solution is obtained. This node candidate can be determined by finding the optimal solution when the number of nodes is small, but it is unknown whether the optimal solution is truly optimal when the number of nodes is large. 1
In the case of, it is sufficient to obtain a local optimal solution, that is, a suboptimal solution.

First, the first method shown in FIG. 10 will be described. As can be seen from FIG. 10, this processing includes processing P41 to processing P59. However, as described above, the index of the node candidate is numbered in ascending order of time, and it is represented by I (j), 0 ≦ j ≦ m.
And In the following description of FIG. 10, j is a loop control variable.

In the process P41, the loop control is performed. There are the following six methods, and the loop control is performed by using any one of the following methods. (1) For odd-numbered j, the processing is performed in order from small to large, and for even-numbered j, processing is performed in order from large to small. (2) For odd j, the processing is performed from the largest to the smallest, and for the even j, the processing is performed from the smallest to the largest. (3) j = 1 to [m / 2] and j = m-1 to [m / 2]
The processing is performed in order up to +1. (4) j = [m / 2] to 1 and j = [m / 2] +1 to m
Process in order up to -1. (5) Perform processing in order from j = 1 to m-1. (6) Perform processing in order from j = m-1 to 1. In the process P42, it is determined whether or not the relationship of I (j-1) <I (j) -1 holds for a loop control variable j for controlling a loop of a series of processes. If this relationship holds, the process shifts to process P43; if not, the process goes to process P4.
Go to 5.

In the process P43, the node candidate I (j) and the node candidate I (j) -1 are temporarily exchanged as shown in FIG. Next, the value of the first objective function after the exchange is calculated. After calculating the function values, the exchanged node candidates are restored.

In process P44, the original first function calculated in process P7 in FIG. 2 from the value of the first objective function calculated in process P43.
The value ΔE (1-) obtained by subtracting the value of the objective function is calculated. Note that ΔE
"1-" in parentheses means to shift to the left by "1", that is, to decrease the index by "1". Processing P4
5, the value of the first objective function is not calculated, and Δ
E (1-) is set to 0. In the process P46, it is determined whether or not the relationship of I (j) +1 <I (j + 1) is established. If this relationship is established, the process proceeds to the process P47. Transition.

In the process P47, the node candidate I (j) and the node candidate I (j) +1 are temporarily exchanged as shown in FIG. 15, and the value of the first objective function at this time is calculated. In the process P48, the process P of FIG.
The value ΔE (1+) obtained by subtracting the value of the original first objective function calculated in step 7
Is calculated. In process P49, ΔE (1+) is forcibly set to 0 without calculating the value of the first objective function.

In process P50, ΔE (1-) <0 and ΔE
It is determined whether (1+) ≧ 0 holds. If this relationship holds, the process moves to process P51; otherwise, the process moves to process P52. In the process P51, the node candidate I (j) is exchanged for the node candidate I (j) -1, and after the exchange, the process returns to the process P41. In the process P52, it is determined whether or not ΔE (1-) ≧ 0 and ΔE (1 +) <0 are satisfied. If this relationship is established, the process proceeds to the process P53. Transition. In the process P53, the node candidate I (j) is exchanged for the node candidate I (j) +1, and after the exchange, the process returns to the process P41.

In the process P54, ΔE (1-) <0 and ΔE (1 +) <
It is determined whether or not the relationship of 0 is established. If this relationship is established, the flow shifts to processing P55; otherwise, the flow returns to processing P41. In process P55, ΔE (1-) ≦ ΔE (1
It is determined whether or not the relationship (+) is established. If this relationship is established, the process proceeds to process P56, and if not, the process proceeds to process P57. In the process P56, the node candidate I (j) is exchanged for the node candidate I (j) -1, and when the exchange is completed, the process returns to the process P41. In the process P57, the node candidate I (j) is exchanged for the node candidate I (j) +1, and after the exchange, the process returns to the process P41. When the above processing is completed for all the loop control variables j, the flow shifts to processing P58.

In process P58, an end determination is made. This end determination is made for all j, from processing P41 to processing P57.
The value of the first objective function when the operation up to
It is executed by determining whether or not the exchange of the node candidates has been performed at all for a value greater than the value obtained by subtracting the threshold value from the value of the objective function or for all j. A series of processes is completed, and the solution at the time of completion is a sub-optimal node candidate. Otherwise, in process P59, the original value of the first objective function is exchanged for the first objective function at the time when the operation is completed, and the process proceeds to process P41.
To P57 is repeated.

The above operation is repeated until the end judgment in the process P58 is established and the value of the first objective function converges. Note that a determination condition based on the number of repetitions of the process may be added to this end determination. However, in this case, the optimum degree may be worse than when the determination condition of the number of repetitions is not added, but the processing can be always completed within a certain time.

Next, the second method shown in FIG. 11 will be described. As can be seen from FIG. 11, this processing includes processing P61 to processing P79. However, as described above, the index of the node candidate is numbered in ascending order of time, and it is represented by I (j), 0 ≦ j ≦ m.
It expresses. As in the case of the description of FIG. 10, j is a loop control variable.

The process P61 is for performing loop control as to whether or not to repeat a series of processes, similarly to the first method in FIG. 10, and the following six methods are available. Loop control is performed using any one of them. (1) For odd-numbered j, processing is performed in the order of small to large, and for even-numbered j, processing is performed in the order of small to large. (2) For odd j, the processing is performed from the largest to the smallest, and for the even j, the processing is performed from the smallest to the largest. (3) j = 1 to [m / 2] and j = m-1 to [m / 2]
The processing is performed in order up to +1. (4) j = [m / 2] to 1 and j = [m / 2] +1 to m
Process in order up to -1. (5) Perform processing in order from j = 1 to m-1. (6) Perform processing in order from j = m-1 to 1. Processes P62 to P70 are the same as processes P42 to P50 of the first method in FIG.

In the process P71, first, the node candidate I (j) is exchanged for the node candidate I (j) -1. Further, the original value of the first objective function is updated to the value of the first objective function calculated at the time of the exchange. Then, after performing this update, the process returns to the process P61. Process P72 is the same as process P52 of the first method in FIG. In the process P73, first, the node candidate I (j) is exchanged for the node candidate I (j) +1. Further, the original value of the first objective function is updated to the value of the first objective function calculated at the time of the exchange. Then, after performing this update, the process returns to the process P61.

Processing P74 and processing P75 correspond to the first processing in FIG.
This is the same as the processing P54 and the processing P55 of the method.
In process P76, the node candidate I (j) is exchanged for the node candidate I (j) -1. Next, the original value of the first objective function is updated to the value of the first objective function calculated at the time of the exchange. Then, after performing this update, the process returns to the process P61.

In process P77, the node candidate I (j) is
Exchange to I (j) +1. Next, the original value of the first objective function is updated to the value of the first objective function calculated at the time of the exchange. Then, after performing this update, the process returns to the process P61. When the above processing is completed for all the loop control variables j, it is determined whether or not the processing P78 is completed. This is the same as the processing P58 of the first method in FIG. About the process P79, the process P59 of the first method of FIG.
Is the same as

In the second method, the first objective function value is changed when the first method has completed a series of processes for the node candidate, whereas the first method is changed every time the node candidate is updated. The value of the objective function is also updated. Which of the first and second methods is superior as a method of determining a sub-optimal node candidate depends on the nature of the data and cannot be said to be one of them. Method seems to be faster.

If the sub-optimal node candidate is determined by the above-described first method according to FIG. 10 or the second method according to FIG. 11, the sub-optimal node candidate is replaced with the interpolation function by the process P9 in FIG. Thus, the same interpolation as in the process P5 is performed. Next, in process P10, the 1
An error between the one-dimensional time-series data and the original one-dimensional time-series data is calculated in the same manner as in the process P6.

In the process P11, from the error calculated in the process P10, the value of the second objective function defined by the weighted addition of the maximum value of the error, the error average, and the error variance is calculated.
This second objective function is an evaluation function of the error relating to the original node. For example, when only the maximum value of the error is a problem, the weight of the maximum error may be set to “1”, and the average and the error variance may be set to “0”. Other than that, when weights are to be uniformly allocated to the maximum error, the error average, and the error variance, as in the case of the first objective function in the process P7, for example, the products of the weights and their values are all equal. If it is determined from the beginning, or if it is determined from the beginning, for example, the values of the weighting factors may all be previously set to “１ ／”.
The ratio may be determined based on the ratio of each weight to the objective function.

In process P12, the second P2 obtained in process P11
A threshold is determined for the objective function value. For example, when the weight of the maximum error is “1” and the error average and error variance are “0”, in the process P1, the value of the approximation accuracy error input first may be used as the threshold. In this case, it is determined whether all the data are within the approximation accuracy. As a result of the threshold value determination, when it is determined that the value is larger than the threshold value, the process shifts to a process P13; otherwise, the process shifts to a process P14.

In process P13, the changed number of nodes is obtained by adding the increment to the original number of nodes. The increment at that time is determined in advance. When the number of nodes is increased by a predetermined amount, the process returns to the process P4, and a series of processes after the determination of the node candidates are performed. repeat.

If it is determined in step P12 that the value of the second objective function is equal to or smaller than the threshold value, the process proceeds to step P14 as described above. Outputs the index number and the data value at that time. The format of the output data in this case is as shown in FIG.

As for the output of the index, there is a method of switching and outputting depending on whether the number of node candidates is less than or equal to half or less than the number of one-dimensional time series data inputted first. In other words, when the number is less than half, the identifier indicating the number and the index number of the node candidate are output.
The identifiers and the indexes other than the node candidates are listed. If the initial time and the time interval of the one-dimensional time series data to be handled are always constant and are known, the initial time and the time interval may be omitted in the output of the process P14.

As described above, according to the first embodiment, 1
Initial node candidates are determined from among the data constituting the dimensional time-series data, and one-dimensional time-series data approximating the original one-dimensional time-series data is generated from the initial node candidates using an interpolation function. Calculate and evaluate these errors, move the node candidates so that the error evaluation falls within the expected range, calculate the sub-optimal node candidates, and use this interpolation function to calculate the sub-optimal node candidates. Generate one-dimensional time-series data that approximates the original one-dimensional time-series data, calculate and evaluate these errors, and if the error evaluation does not fall within the expected range, increase the number of nodes. By repeating the process of, optimization is performed on both the position and number of nodes,
Since data other than nodes is not transmitted, the data is compressed, so that compression can be performed in accordance with the properties of given one-dimensional time-series data. Further, since the compression ratio of the data is controlled by the approximation accuracy, the error after decompression can be grasped in advance.

Embodiment 2 In the first embodiment, the one-dimensional time-series data compression processing is realized by software.
This data compression processing may be realized by dedicated hardware. FIG. 4 shows a one-dimensional time-series data compression apparatus in which the processing flow of FIG. 1 is implemented as dedicated hardware. The node candidate calculating means 10b for calculating a candidate of a node through which an interpolation function approximating the one-dimensional time-series data passes is a node candidate calculating means 10a.
Position optimization means 10c for optimizing the position of the node candidate calculated by the above-described method. The error between the interpolation function passing through the node obtained by the node position optimization means 10b and the original one-dimensional time series data is input to Determining means for determining whether or not a value corresponding to the approximation accuracy value input in 40a is satisfied;
0d is a node number changing means for changing the number of nodes when the determination means 10c determines that the approximation accuracy is not satisfied. 40b is an interpolation function passing through the node and the original one-dimensional time series. The error from the data is input means 40a.
Output means for outputting this node and its index as compression information when a value corresponding to the approximation accuracy value input in step (1) is satisfied.

Next, the operation will be described. As shown in FIG. 4, one-dimensional time-series data to be compressed and its approximation accuracy value are input to input means 40a, and node candidate calculating means 10a outputs all the one-dimensional data constituting the one-dimensional time-series data. Among them, a node candidate is calculated, and a predetermined interpolation function passes through the node data to calculate a node candidate that can generate one-dimensional time series data approximating the original one-dimensional time series data, and optimizes the position of the node. In the means 10b, the node candidate is moved to optimize the position of the node. In the determination means 10c, the error between a predetermined interpolation curve passing through the optimized node candidate and the original one-dimensional time-series data is calculated. It is determined whether or not the value based on the value is within the range of the approximation accuracy value input by the input unit 40a. If the value is within the range of the approximation accuracy, the node position is immediately optimized by the output unit 40b. Node candidate is output as one-dimensional time series data obtained by compressing the index.

If the judging means 10c finds out of the range of the approximation accuracy, the number of nodes changing means 10d optimizes the number of nodes by appropriately increasing or decreasing the number of nodes. After the number of nodes is changed by the node number changing means 10d, the process returns to the node candidate calculating means 10a to calculate the node candidates again, and the same processing is repeated thereafter.

FIG. 5 shows a more detailed configuration of the one-dimensional time-series data compression apparatus of FIG. In the figure, 40
a is input means for inputting one-dimensional time series data to be data-compressed from outside and its approximation accuracy; 11 is an index adding means for adding an index to the one-dimensional time series data; and 12 is this one-dimensional time series data. Initial node number calculating means for calculating the initial number of nodes passing by the interpolation function approximating the data, 13 is a node candidate determining means for determining candidates of nodes passing by the interpolation function, and 14 is an interpolation function passing through the node candidates Interpolation executing means for interpolating data between node candidates according to the following formula: 15 is an error calculating means for calculating an error between the one-dimensional time-series data obtained by the interpolation function and the original one-dimensional time-series data; A first objective function calculating means 17 for calculating a first objective function value, which is an evaluation function of the error, is a sub-optimal node for appropriately moving the node candidate to determine a sub-optimal node candidate. A candidate determining means 18 is an interpolation executing means for interpolating data between the sub-optimal node candidates by an interpolation function passing through the sub-optimal node candidates, and 19 is a one-dimensional time series data obtained by the interpolation function and an original one-dimensional data. Error calculating means for calculating an error between the time series data, 20 is a second objective function calculating means for calculating a second objective function value which is an evaluation function of the error, and 21 is a function value of the second objective function. Is a threshold value determining means for determining whether or not exceeds a threshold value according to the approximation accuracy of the original one-dimensional time series, and a threshold value 22 corresponding to the function value of the second objective function corresponding to the approximation accuracy of the original one-dimensional time series data A node number changing means 40b for changing the number of nodes when the value exceeds the threshold value, a sub-optimal node candidate is selected when the function value of the second objective function does not exceed a threshold value according to the approximation accuracy of the original one-dimensional time-series data. Compressed data of original one-dimensional time series data As an output means for outputting with the index.

Next, the operation will be described. First, the input means 40a inputs one-dimensional time-series data to be data-compressed and an approximation accuracy value of an interpolation function that approximates the data. The index adding means 11 adds an index to the one-dimensional time-series data in order of the time. As this time, a sample time, an occurrence time, an input time, or the like of the one-dimensional time-series data can be used. It should be noted that the index may use data that increases sequentially or data that decreases sequentially instead of the time. The initial node number calculation means 12 calculates the initial node number. The initial value of the number of nodes used at that time is determined according to the type of the interpolation function.
The initial value may be set, and therefore, for example, this can be calculated by previously determining the ratio to the initial number of data. Here, as in the case of FIG. 2, the initial number of nodes is calculated as an initial value of the number of nodes to be used in the form of 1 / a of the total number of one-dimensional time-series data (where a> 0). It shall be.

The node candidate determining means 13 always includes data at the beginning and end of the one-dimensional time-series data to be compressed, and selects data at random intervals for the remaining data. The node candidates are determined so that the total is equal to the calculated number of nodes.
This operation is performed in the same manner as that shown in FIG. 13 or FIG. The operation performed by the node candidate determining means 13 is to determine the initial value of the position of the node candidate, and it is known that it is effective to use random numbers for this kind of problem. Even in the case of, a better value is experimentally obtained when the node positions are selected using random numbers than when the nodes are selected at approximately equal intervals.

The interpolation executing means 14 generates data for interpolating between the node candidates by an interpolation function using the index number as an independent variable, and obtains one-dimensional time-series data approximating the original one-dimensional time-series data. , And an error between this and the original one-dimensional time-series data. As the interpolation function, a series expansion expression using a spline function or a discrete Fourier transform, a series expansion expression using a discrete cosine transform, or the like can be used as in the case of FIG.

In the error calculating means 15, as shown in FIG.
An error between the one-dimensional time-series data other than the node candidates and the interpolation function is calculated. In the case of FIG. 14, the calculation of the error is performed using the absolute value error, but the calculation of the error may be performed using a square error or the like.

The first objective function calculating means 16 calculates the value of the first objective function from the error calculated by the error calculating means 15. This first objective function can be calculated by first obtaining the maximum value of the error calculated by the error calculating means 15, the error average, and the error variance, and weighting and adding them.

The sub-optimal node candidate determining means 17 repeatedly changes the node candidates so that the value of the first objective function is minimized, and determines the sub-optimal node candidates. Similarly, there are two methods, the first method shown in FIG. 10 and the second method shown in FIG.

When the sub-optimal node candidates are determined by the first method according to FIG. 10 or the second method according to FIG. 11, the sub-optimal node candidates are replaced by the interpolation function Thus, interpolation is performed in the same manner as in the interpolation executing means 14. Next, the error calculator 19 calculates an error between the one-dimensional time-series data obtained by interpolation and the original one-dimensional time-series data in the same manner as the error calculator 15.

The second objective function calculating means 20 calculates, from the error calculated by the error calculating means 19, the value of the second objective function defined by weighted addition of the maximum value of the error, the error average and the error variance. . This second objective function is an evaluation function of the error relating to the original node. And the value of the weight is
For example, when only the maximum value of the error is a problem, the weight of the maximum error is “1”, and the error average and error variance are “0”.
And it is sufficient. In addition, the first objective function calculating means 1
In the same way as in the case of the first objective function in No. 6, when weights are to be equally allocated to the maximum error, the error average, and the error variance, for example, the product of each weight and their values may be determined to be equal, or from the beginning, When it is determined, the values of the weighting factors may be previously determined to be all "1/3", for example, and based on the ratio to each weight at the time of the first objective function. You may decide.

The threshold value judging means 21 makes a threshold value judgment for the second objective function value obtained by the second objective function calculating means 20. For example, when the weight of the maximum error is “1” and the error average and error variance are “0”, the input means 40a
In, the approximation accuracy error input first may be used as the threshold. In this case, it is determined whether all the data are within the approximation accuracy. As a result of the threshold judgment,
If it is determined that the value is larger than the threshold value, the number of nodes changing means 22
Otherwise, the process proceeds to the output means 40b.

The node number changing means 22 obtains the change in the node number by adding an increment to the original node number. The increment at that time is determined in advance. Then, when the number of nodes is increased by a predetermined amount, the process returns to the node candidate determining means 13, and a series of processes after the determination of the node candidates is performed. These series of processes are repeated.

When the threshold value determining means 21 determines that the value of the second objective function is equal to or smaller than the threshold value, as described above, the output means 40
The output means 40b outputs the initial time and the amount of time interval, the index number of the obtained node candidate, and the data value at that time. The format of the output data in this case is as shown in FIG.

As for the output of the index, there is a method of switching and outputting depending on whether the number of node candidates is less than or equal to half or less than the number of one-dimensional time series data inputted first. In other words, when the number is less than half, the identifier indicating the number and the index number of the node candidate are output.
The identifiers and the indexes other than the node candidates are listed. When the initial time and the time interval of the one-dimensional time series data to be handled are always constant and known, the initial time and the time interval may be omitted in the output by the output unit 40b.

As described above, according to the second embodiment, 1
Initial node candidates are determined from among the data constituting the dimensional time-series data, and one-dimensional time-series data approximating the original one-dimensional time-series data is generated from the initial node candidates using an interpolation function. Calculate and evaluate these errors, move the node candidates so that the error evaluation falls within the expected range, calculate the sub-optimal node candidates, and use this interpolation function to calculate the sub-optimal node candidates. Generate one-dimensional time-series data that approximates the original one-dimensional time-series data, calculate and evaluate these errors, and if the error evaluation does not fall within the expected range, increase the number of nodes. By repeating the process of, optimization is performed on both the position and number of nodes,
Since data other than the nodes is not transmitted and the processing for compressing the data is performed by the dedicated hardware, the compression in accordance with the property of the given one-dimensional time-series data can be performed quickly. Further, since the compression ratio of the data is controlled by the approximation accuracy, the error after decompression can be grasped in advance.

Embodiment 3 FIG. Next, a one-dimensional time-series data compression method according to the third embodiment of the present invention will be described with reference to the drawings. The third embodiment is different from the first embodiment.
In the one-dimensional time-series data compression method of
If a series of data, ie, one-dimensional time-series data that falls within a range that can be regarded as substantially zero, continues, the processing can be omitted.

FIG. 6 shows a processing flow of the one-dimensional time-series data compression method according to the third embodiment of the present invention. As shown in FIG. 6, the entire processing is the same as that shown in FIG.
If the one-dimensional time-series data input in step a is within the approximation accuracy, the process immediately proceeds to the output process P4b. The processing is performed.

FIG. 7 shows the processing of FIG. 6 in more detail. The processing of FIG. 7 is executed by, for example, the computer of FIG. 3 from the eleventh step S11 to the twentieth step S20. In this case, a program corresponding to the processing in FIG. 7 is stored in the main memory 3 of the computer in FIG. 3 in advance or by being loaded from a program recording medium or the like. The eleventh step S11 is performed from the processing P21 to the processing P2.
The twelfth step S12 is processing P24, the thirteenth step S13 is processing P25, and the fourteenth step S14 is processing S2.
6 and processing S27, the fifteenth stage S15 is processing P28
The sixteenth step S16 is a process P29, and the seventeenth step S1
7 is a process P30 and a process P31, an eighteenth stage S18 is a process P32, a nineteenth stage S19 is a process P25 to a process P34, and a twentieth stage S20 is a process P35.

Each processing configured as described above will be described in detail. The processing from processing P21 to processing P23 is the processing P of the first embodiment of the present invention shown in FIG.
The processing is the same as the processing from 1 to P3. Processing P
Regarding 24, it is determined whether or not the absolute values of all the data values of the given one-dimensional time-series data are lower than the approximation accuracy input in the process 21. At this time, when it is determined that the approximation accuracy is equal to or lower than the input accuracy, it corresponds to a so-called zero column. In this case, the information compression method of the third embodiment does not perform information compression. Then, the process immediately proceeds to the process P35. On the other hand, when the absolute value of at least one data value is greater than the approximation accuracy, the processing shifts to processing P25.

The processing from processing P25 to processing P34 is the same as the processing from processing P4 to processing P13 in FIG. Regarding the process P35, the thirteenth stage S
If the process has passed through the thirteenth to nineteenth steps S19, the data is output in the format of FIG. On the other hand, when the process directly proceeds to the process P35 by the process P24, the output is performed in the format of (b) in FIG. That is, it outputs an initial time, a time interval, and an identifier indicating that all data values are “0”.

As described above, according to the third embodiment, if the data falls within a range that can be regarded as “0” within the approximation accuracy, the compression processing can be omitted.
When data that can be regarded as “0” is continuous, the processing can be omitted. Particularly when the number of data is large, there is an effect that higher-speed data compression processing can be performed.

Embodiment 4 In the third embodiment, the one-dimensional time-series data compression processing is realized by software.
This data compression processing may be realized by dedicated hardware. FIG. 8 shows a one-dimensional time-series data compression apparatus in which the processing flow of FIG. 6 is implemented as dedicated hardware. In the figure, the same reference numerals as those in FIG. 4 denote the same or corresponding elements. Reference numeral 10f denotes a judgment means which is provided between the input means 40a and the node candidate calculating means 10a. Only when it does not fall within the approximation accuracy, similarly to FIG. 6, the processing shifts to the node candidate calculating means 10a, and processing switching control is performed so as to perform a series of data compression processing.

FIG. 9 shows a more detailed configuration of the one-dimensional time-series data compression apparatus shown in FIG.
The same reference numerals indicate the same or corresponding elements. Numeral 23 denotes an approximation accuracy determination means provided between the input means 40a and the index addition means 11, and the determination means 10 shown in FIG.
f, input means 40a and index adding means 11
And is provided between them.

Next, the operation of FIG. 9 will be described. The one-dimensional time-series data compression device of FIG. 9 has an in-approximation-accuracy determining unit 23 between the input unit 40a and the index adding unit 11, and the in-approximation-in-determining unit 23 receives the input from the input unit 40a. It is determined whether or not the obtained one-dimensional time-series data falls within the approximation accuracy. If the one-dimensional time-series data falls within the approximation accuracy, the data compression operation by the present one-dimensional time-series data compression apparatus is not performed. Output means 40
Only when the processing shifts to b and does not fall within the approximation accuracy, similarly to FIG. 6, the processing shifts to the index adding means 11 and performs processing switching control so as to perform a series of data compression processing.

As described above, according to the fourth embodiment, when the data falls within a range that can be regarded as “0” within the approximation accuracy, the compression processing can be omitted.
When data that can be regarded as “0” is continuous, the processing can be omitted. Especially when the number of data is large, higher-speed data compression processing becomes possible, and these processings are performed by dedicated hardware. There is an effect that the speed can be further increased.

Embodiment 5 FIG. In the following, one data compressed by the compression method according to the first or third embodiment will be described.
A method for expanding the dimensional time-series data will be described. In the fifth embodiment, first, a description will be given of a case where it is guaranteed that compressed data is supplied only in the format of FIG.

FIG. 17 shows one-dimensional time-series data compressed by the compression method according to the first embodiment, that is, FIG.
5 shows a method of decompressing data when compressed data is supplied only in the format of. This extension method is 3
In the figure, P5a is an input process for inputting compressed data or the like compressed by the one-dimensional time-series data compression method according to the first embodiment, and P101a interpolates and decompresses compressed data using an interpolation function. Data decompression processing, P5b, is output processing for outputting decompressed one-dimensional time-series data.

Next, the processing method will be described. In the input process P5a, the compressed data compressed by the one-dimensional time-series data compression method according to the first embodiment and the number of data to be generated when the data is expanded are input. Next, in the data decompression processing P101a, decompression is performed by interpolating the compressed data using the same interpolation function used when compressing the data. Then, in the output process P5b, the one-dimensional time-series data expanded by the data expansion process P101a is output.

FIG. 18 shows the expansion method of FIG. 17 in more detail. In the figure, a first stage S31 is composed of an input process P101 similar to the input process P5a in FIG. The second stage S32 includes a data interpolation process P102 for interpolating compressed data, a data calculation process P103 for calculating decompressed data, and a time calculation process P104 for calculating a time corresponding to the decompressed data.
The third step S33 includes an output process P105 similar to the output process P5b in FIG.

FIG. 18 shows the detailed processing.
7 is performed by the computer shown in FIG.
The processing is performed in steps S31 to S33. In this case, the main memory 3 of the computer in FIG.
The program corresponding to the process of No. 7 is stored in advance or by being loaded from a program recording medium.

Next, the decompression method will be described. First, in the first step S31, the input data P101 is used to input the compressed data compressed by the one-dimensional time-series data compression method according to the first embodiment and the number of data to be generated when the data is expanded.

Next, in the second step S32, the data interpolation processing P102 is used to interpolate the compressed data using the same interpolation function used when compressing the data, thereby achieving data continuity. The required number of data is calculated from the serialized data, and the time calculation process P104 calculates the number of data requiring the time from the initial time and the time interval. However, the interpolation function is a function that uses an index as an independent variable as in the case of compression, and generates an interpolation function using the value of the index sequence of the compressed data.

Then, in a third step S33, the data calculated in the second step S32 and the time are output as one-dimensional time-series data obtained by extending the time by the output process P105. As can be seen from the above expansion method, when restoring one-dimensional time-series data, the number of data can be expanded to a number different from the original one. In other words, it means that the time of the one-dimensional time-series data can be changed, and that the control can be performed by the number of input data.

As described above, according to the fifth embodiment, the one-dimensional time-series data compressed by the method of the first embodiment can be expanded. There is an effect that a one-dimensional time-series data decompression method can be obtained which can be arbitrarily increased or decreased with respect to the one-dimensional time-series data and in which case the number of generated data can be increased or decreased without deteriorating the properties of the data.

Embodiment 6 FIG. In the fifth embodiment, the one-dimensional time-series data decompression processing is realized by software.
This data decompression processing may be realized by dedicated hardware. FIG. 19 shows a one-dimensional time-series data decompression device in which the processing flow of FIG. 17 is implemented as dedicated hardware. One-dimensional time-series data compressed by the compression device of the second embodiment, that is, (a) in FIG. 3) shows a data decompression device in the case where compressed data is supplied only in the format of (1). In the figure, 50a is input means for inputting compressed data or the like compressed by the one-dimensional time-series data compression apparatus according to the second embodiment, 20a is data expansion means for interpolating and expanding compressed data by an interpolation function, and 50b is expansion. Output means for outputting the obtained one-dimensional time-series data.

Next, the operation will be described. The input means 50a inputs the compressed data compressed by the one-dimensional time-series data compression device according to the second embodiment and the number of data to be generated when the data is expanded. Next, the data decompression means 20a interpolates and decompresses the compressed data using the same interpolation function used when compressing the data. Then, the output means 50b outputs the one-dimensional time-series data expanded by the data expansion means 20a.

FIG. 20 shows the configuration of the decompression device shown in FIG. 10 in more detail. In FIG.
Ninth input means 50a. Reference numeral 21 denotes data interpolation means for performing data interpolation processing on input data, reference numeral 22 denotes data calculation means for calculating decompressed data from the interpolated data, and reference numeral 23 denotes time calculation means for calculating a time corresponding to the data. . Reference numeral 50b denotes an output unit configured similarly to the output unit 50b of FIG.

Next, the operation will be described. First, the input means 50a inputs the compressed data compressed by the one-dimensional time-series data compression device according to the second embodiment and the number of data to be generated when the data is expanded. Next, the data interpolation means 21 interpolates the compressed data using the same interpolation function used when compressing the data,
The data continuity is calculated, the required number of data is calculated by the data calculation means 22 from the continuous data, and the time calculation means 23 converts the data requiring the time from the initial time and the time interval. Calculate for the number. However, the interpolation function is a function that uses an index as an independent variable as in the case of compression, and generates an interpolation function using the value of the index sequence of the compressed data.

Then, the output means 50b outputs the calculated data and time as expanded one-dimensional time-series data. As described above, according to the sixth embodiment, the one-dimensional time-series data information compressed by the apparatus according to the second embodiment can be decompressed at high speed by dedicated hardware. The original one-dimensional time-series data can be arbitrarily increased or decreased, and the number of generated data can be increased or decreased without deteriorating the properties of the data.

Embodiment 7 Next, a method for expanding the one-dimensional time-series data compressed by the compression method according to the third embodiment will be described. In the seventh embodiment, a case will be described in which data of the format of FIG. 16A and data of the format of FIG.

FIG. 21 shows one-dimensional time-series data compressed by the compression method according to the third embodiment, that is, FIG.
16 and the format of FIG. 16 (b) are mixed and data is supplied. This stretching method is composed of four steps.
The same reference numerals as those in FIG. 17 indicate the same or corresponding components. P
101b is a data format discriminating process for discriminating the format of the compressed data, and P101c is a 0 data decompressing process for decompressing all the compressed data when it is discriminated to be "0".

Next, the decompression method will be described. FIG.
When the data is supplied in the format of FIG. 6 (a), the data format discrimination processing P101b converts the data into the data decompression processing P1.
01a, and thereafter decompresses the data in the same manner as in FIG. 17, and outputs the data through output processing P5b. In contrast, FIG.
When the data is supplied in the format of FIG. 6 (b), the data format discrimination processing P101b converts the data to the 0 data decompression processing P101b.
The data is passed to 101c, and all data of "0" is generated for a predetermined period, and is output by the output process P5b as in FIG.

FIG. 22 shows the expansion method of FIG. 21 in more detail. The processing of FIG. 21 whose details are shown in FIG. 22 is executed by, for example, the computer of FIG. In this case, a program corresponding to the processing in FIG. 22 is stored in the computer in FIG. 3 in advance or by being loaded from a program recording medium.

In the figure, the first stage S41 comprises an input process P101 similar to the input process P101 of FIG. The second step S42 is a data format determination process P10
6,0 data calculation process P107, time calculation process P108
It is composed of The third step S43, like the second step S32 in FIG. 18, includes a data interpolation process P102, a data calculation process P103, and a time calculation process P104. The third step S44 includes an output process P105 similar to the output process P105 in FIG.

Next, a description will be given of the extension method. First, in a first stage S41, the input data P101 is used to input the compressed data compressed by the one-dimensional time-series data compression method and the number of data when decompressed.

Next, in the second step S42, in the data format determination process P106, the format of the compressed data is determined, and in the case of the format shown in FIG. 16B, that is, the compressed data is all "0". In the case of the identifier indicating “0”, the same number of data “0” is calculated by the 0 data calculation process P107, and the time is calculated from the initial time and the time interval by the number of data by the time calculation process P108. The calculated "0" data and the time are stored in the fourth step S44.
Is output as one-dimensional time-series data by the output process P105.

On the other hand, in the third step S43, when it is determined in the second step S42 that the compressed data is not an identifier indicating that all the data is "0", that is, in the case of the format shown in FIG. At this time, as in the second step S32 in FIG. 18, the compressed data is interpolated by the interpolation function used at the time of compression, the data is made continuous, and the number specified by the input processing from the continuous data is obtained. The data of the minute is calculated, and the time is calculated from the initial time and the time interval by the same number as the data.
However, the interpolation function is a function that uses an index as an independent variable, as in the case of compression, and generates an interpolation function using the value of the index sequence of the compressed data.

Then, in a fourth step S44, FIG.
Of the second step S42 or the third step S42
The data and time calculated in step S43 are output as data-expanded one-dimensional time-series data.

As can be seen from the above expansion method, when restoring one-dimensional time-series data, the number of data can be expanded to a number different from the original one. This is, in other words, 1
This means that the time of the dimensional time-series data can be changed, and that the control can be performed by the number of input data.

As described above, according to the seventh embodiment, the one-dimensional time-series data compressed by the method of the third embodiment can be expanded, and the number of data to be generated at the time of the expansion is reduced by the original number. There is an effect that a method of expanding one-dimensional time-series data can be obtained which can be arbitrarily increased or decreased with respect to the one-dimensional time-series data, and in which case the number of generated data can be increased or decreased without deteriorating the properties of the data.

Embodiment 8 FIG. In the seventh embodiment, the one-dimensional time-series data decompression processing is realized by software.
This data decompression processing may be realized by dedicated hardware. FIG. 23 shows a one-dimensional time-series data decompression device in which the processing flow of FIG. 21 is implemented as a dedicated hardware. One-dimensional time-series data compressed by the compression device of the fourth embodiment, that is, FIG. 16) and the format shown in FIG. 16 (b) are mixed and data is supplied. In the figure, the same reference numerals as those in FIG. 19 indicate the same or corresponding components. 20b is a data format discriminating means for discriminating the format of the compressed data, and 20c is a 0 data decompressing means for decompressing all the compressed data when it is discriminated to be "0".

Next, the expansion operation will be described. FIG.
When data is supplied in the format of FIG. 6 (a), the data format discriminating means 20b passes the data to the data decompressing means 20a, and thereafter decompresses the data as in FIG. 19 and outputs the data by the output means 50b. .

On the other hand, when data is supplied in the format shown in FIG. 16 (b), the data format discriminating means 20b passes the data to the 0 data decompressing means 20c, and all data of "0" are kept for a predetermined period. Data is generated and output by the output means 50b as in FIG.

FIG. 24 shows the expansion device of FIG. 23 in more detail. In the figure, the same reference numerals as those in FIG. 20 indicate the same or corresponding parts. 24 is a data format determining means for determining the format of the input data, 25 is "0"
Numeral 0 data calculating means for calculating data, 26 is a time calculating means for calculating the time corresponding to the “0” data. Next, the decompression operation will be described. First, the input means 50a
Thus, the compressed data compressed by the one-dimensional time-series data compression device and the number of data when decompressed are input.

Next, in the data format determining means 24,
The format of the compressed data is determined. In the case of the format shown in FIG. 16B, that is, in the case of an identifier indicating that all the compressed data is “0”, the number of data The same number of “0” is calculated, and the time calculating means 2
According to 6, the time is calculated for the number of data from the initial time and the time interval. The calculated “0” data and the time are output as one-dimensional time-series data by the output unit 50b.

On the other hand, when the data format determining means 24 determines that the compressed data is not an identifier indicating that all the data is "0", that is, the data in the format of FIG. In this case, similarly to FIG. 20, the compressed data is interpolated by the interpolation function used for compression,
The data is made continuous, the number of data specified by the input means 50a is calculated from the continuous data, and the time is calculated from the initial time and the time interval by the same number as the data. However, the interpolation function uses an index as an independent variable and generates an interpolation function using the value of the index sequence of the compressed data, as in the case of compression. Then, the output means 50b outputs the calculated data and time as one-dimensional time-series data obtained by expanding the data, as in FIG.

As described above, according to the eighth embodiment, the one-dimensional time-series data compressed by the apparatus according to the fourth embodiment can be decompressed at high speed by dedicated hardware, and is generated when the decompression is performed. The number of data can be arbitrarily increased or decreased with respect to the original one-dimensional time-series data, and the number of generated data can be increased or decreased without deteriorating the properties of the data.

Embodiment 9 FIG. Note that the present invention is not only applicable to one-dimensional time-series data,
That is, compression and decompression of a plurality of one-dimensional time series data can be realized by applying the same compression and decompression methods and compression and decompression devices. For example, compression of a plurality of one-dimensional time-series data can be performed by repeatedly using the compression method according to the first or third embodiment of the present invention or the compression device according to the second or fourth embodiment.

In the ninth embodiment, a case where such multidimensional time-series data is
This is explained using on Data Compression as an example. This Moti
As described above, on Data Compression is a method for compressing the amount of multidimensional time-series data expressing human motion when a human is regarded as a rigid articulated object and its motion is expressed.

Motion Data is a translation vector of a representative point position of a rigid articulated object modeled on a person, a rotation amount of a posture vector with respect to a coordinate axis in a three-dimensional space, a translation vector of each joint (joint), and a local coordinate system. Is constituted by the amount of rotation with respect to each coordinate axis.

[0193] That is, when a joint number of rigid articulated object m, the time series length and n, Motion Data is _{{M i = (Cx i,} Cy i, Cz i, θ i Cx, θ i Cy,
θ _i ^Cz , x _i ^jt0 , y _i ^jt0 , z _i ^jt0 , θ _i ^jtx0 ,
θ _i ^jty0 , θ _i ^jtz0 ,…, x _i ^jtm-1 , y _i ^jtm-1 , z _i
^jtm-1 , θ _i ^jtxm-1 , θ _i ^jtym-1 , θ _i ^jtzm-1 ) | i =
0, 1,..., N−1}. However, in this example, the order of rotation is x axis, y
Axes, and set the order of _{z-axis, Cx i, Cy i, Cz} i root, i.e. serving as a reference point of the coordinate values of the position on the rigid ^{_{body, θ i Cx, θ i Cy}} , θ i Cz is the joint Attitude control angles, x _i ^jt0 , y _i ^jt0 , and z _i ^jt0 are joint slide amounts, θ _i ^jtx0 , θ _i ^jty0 , θ _i ^jtz0 , ..., x _i ^jtm-1 , y
_i ^jtm-1 , z _i ^jtm-1 , θ _i ^jtxm-1 , θ _i ^jtym-1 , θ _i
^jtzm-1 is the rotation angle of the m joints about the x, y, and z axes.

FIG. 25 shows this Motion Data compression method. In FIG. 25, P200 represents Motion Data input processing for inputting Motion Data, and P201 represents Motion Data which is multidimensional time-series data as many as the number of dimensions. Multidimensional time-series data decomposition processing for decomposing into one-dimensional time-series data, P
A compression unit 202 compresses the decomposed one-dimensional time-series data using the compression method according to the first or third embodiment.
Dimensional time-series data compression processing, P203: determination processing for determining whether or not compression of all the one-dimensional time-series data having the same number of dimensions has been completed, and P204: output processing for outputting compressed multidimensional time-series data. It is. The processing in FIG. 25 is executed by, for example, the computer in FIG. In this case, the main memory 3 of the computer in FIG.
Is stored in advance or by loading from a program recording medium.

Next, the processing will be described. First, by input processing P200, Mo as multidimensional time-series data
Enter tion data. Next, in the decomposing process P201, the Motion Data is decomposed into one-dimensional time-series data for each element, and an index number is given to each one-dimensional time-series data.

The processing after the decomposition processing P201 is the same as the one-dimensional time-series data compression method of the first or third embodiment. That is, in the one-dimensional time-series data compression process P202 after the decomposition process P201, the compression process is performed on each of the decomposed one-dimensional time-series data by the same compression method as in the first or third embodiment. . Then, when it is determined in the determination process P203 that compression processing has been performed on all the one-dimensional time-series data,
Through the output process P204, each compressed one-dimensional time-series data, that is, compressed multi-dimensional Motion Data is output.

As described above, according to the ninth embodiment, the multi-dimensional time-series data is compressed into a plurality of one-dimensional time-series data, and each of the one-dimensional time-series data is compressed according to the first or the first embodiment. Since the compression is performed by applying the same compression method as that of No. 3, the error between the original one-dimensional time-series data and the interpolation function is reduced with respect to certain one-dimensional time-series data so that the data is not compressed. Even if there is a simple section, since there is often a data that can be compressed among the remaining one-dimensional time-series data in the same section as this section,
As a whole, multi-dimensional time-series data can be compressed to about 1/4 to 1/5 of the original. As an example of the multidimensional time series data, in an experiment on the case where time series data of joint angles of a rigid articulated object (human) is used, the compression ratio depends on the approximation accuracy.
8 to 0.264 could be obtained.

In the case of such one-dimensional time-series data representing the motion of each joint angle of the rigid articulated joint, errors accumulate toward the tip of the motion. Therefore, when the approximation accuracy is kept constant, it is necessary to make the value smaller than the value used for the one-dimensional time-series data having no such relationship. In this case, however, the overall compression ratio decreases. Become.
In order to avoid such problems, the approximation accuracy is not fixed, but the approximation accuracy of the original joint of the rigid articulated object is set smaller than usual, and the approximation accuracy is gradually increased toward the beginning. To reduce the compression ratio,
This can be prevented more than the case where the approximation accuracy is kept constant. Also, for one-dimensional time-series data with unequal intervals with respect to time, the multi-dimensional time-series data compression method of the ninth embodiment is applied by using time and data as independent one-dimensional data. What is necessary is just to compress independently.

Embodiment 10 FIG. In the ninth embodiment, the compression processing of multidimensional time-series data is realized by software, but this data compression processing may be realized by dedicated hardware. FIG. 26 shows a multi-dimensional time-series data compression apparatus in which the processing flow of FIG. 25 is implemented as dedicated hardware.
tion Data input means, 51 is a multidimensional time series data decomposing means for decomposing Motion Data, which is multidimensional time series data, into one-dimensional time series data of the same number as that dimension, and 52 is a decomposed one-dimensional time series. Compress data using a configuration similar to that of the compression apparatus of the second or fourth embodiment.
Dimensional time-series data compression means 53; determination means for determining whether or not compression of all the one-dimensional time-series data of the same number as the number of dimensions has been completed; 100b output for outputting compressed multi-dimensional time-series data Means.

Next, the operation will be described. First, Mo as multidimensional time series data is input by the input unit 100a.
Enter tion data. Next, the Motion Data is decomposed into one-dimensional time-series data for each element by the multidimensional time-series data decomposing means 51, and an index number is given to each one-dimensional time-series data. The operation after the decomposing unit 51 is the same as the operation of compressing the one-dimensional time-series data according to the second or fourth embodiment. That is, 1 after the disassembly means 51
The one-dimensional time-series data after decomposition is subjected to compression processing by the one-dimensional time-series data compression means 52 by the same compression operation as in the second or fourth embodiment.

When the determining means 53 determines that the compression processing has been performed on all the one-dimensional time-series data, the output means 100b compresses each of the one-dimensional time-series data, that is, the compressed multi-dimensional time-series data. Output dimensional Motion Data.

As described above, according to the tenth embodiment,
The multidimensional time-series data is compressed into a plurality of one-dimensional time-series data, and compression is performed by applying the same compression operation as in the second or fourth embodiment to each one-dimensional time-series data. Therefore, the compression operation can be performed at high speed by the dedicated hardware, and the error between the original one-dimensional time-series data and the interpolation function is so small that certain one-dimensional time-series data is not compressed. Even if there is a simple section, since there are many one-dimensional time-series data that can be data-compressed among the remaining one-dimensional time-series data in many cases with respect to the same section as this section, when viewed as a whole multi-dimensional time-series data, It becomes possible to perform data compression to about 1/5. In an experiment on the case where, for example, the time series data of the joint angles of a rigid articulated object (human) is used as the multidimensional time series data, the compression ratio is 0.168 to 0.264, although it depends on the approximation accuracy. I got it.

In the case of such one-dimensional time-series data representing the motion of each joint angle of the rigid multi-joint, errors are accumulated toward the tip of the motion. Therefore, when the approximation accuracy is kept constant, it is necessary to make the value smaller than the value used for the one-dimensional time-series data having no such relationship. In this case, however, the overall compression ratio decreases. Become.
In order to avoid such inconveniences, the approximation accuracy should not be constant, but the approximation accuracy should be smaller for the original joint of the rigid articulated object than in the normal case, and the approximation accuracy should be increased toward the beginning. By using this, it is possible to prevent the compression ratio from lowering than when the approximation accuracy is kept constant. Further, for one-dimensional time-series data with unequal intervals with respect to time, the multidimensional time-series data compression apparatus of the tenth embodiment is applied by using time and data as independent one-dimensional data. What is necessary is just to compress independently.

Embodiment 11 FIG. In the eleventh embodiment,
This embodiment deals with a method for expanding multidimensional time-series data compressed according to the ninth embodiment. FIG. 27 shows an example of a method of decompressing MotionData compressed by the compression method of FIG. 25. In FIG. 27, P300 denotes a multidimensional compressed data input process for inputting the compressed Motion Data.
P301 converts the compressed multidimensional time-series data into a plurality of
A multidimensional compressed data decomposing process for decomposing into one-dimensional compressed time-series data. P302 is a one-dimensional one that decompresses the decomposed one-dimensional time-series data using the decompression method of the fifth or seventh embodiment. Time series data decompression processing, P30
Reference numeral 3 denotes a determination process for determining whether or not expansion of a series of one-dimensional time-series data has been completed, and reference numeral P304 denotes output processing for outputting a series of expanded one-dimensional time-series data. This FIG.
Is executed by the computer shown in FIG. 3, for example. In this case, a program corresponding to the processing in FIG. 27 is stored in the main memory 3 of the computer in FIG. 3 in advance or by being loaded from a program recording medium or the like.

Next, the processing flow will be described. First, by the input process P300, the compressed Motion Data
Enter Next, in the decomposing process P301, the compressed Motion Data is decomposed into one-dimensional compressed time-series data for each element, and an index number is given to each compressed one-dimensional time-series data. The processing after the decomposition processing P301 is the same as the one-dimensional time-series data expansion method of the fifth or seventh embodiment. That is, in the one-dimensional time-series data decompression process P302 after the decomposition process P301, the decompression process is performed on each of the decomposed one-dimensional time-series data by the same decompression method as in the fifth or seventh embodiment. .

Then, when it is determined by the determining process P303 that the decompression process has been performed on all the one-dimensional time-series data, each of the compressed one-dimensional data is determined by the output process P304.
Dimensional time series data, that is, expanded multi-dimensional Motion Dat
Output a. As described above, according to the eleventh embodiment, the compressed multidimensional time-series data is decomposed into a plurality of one-dimensional time-series data, and each one-dimensional time-series data is used in the fifth or the fifth embodiment. Since decompression is performed by applying the same decompression method as in No. 7, the decompression process can be performed on multidimensional compressed time-series data.

When the expansion is performed, the number of data to be generated can be set to a number different from the original data. In particular, in the case of expanding Motion Data, the number of generated data is larger than that of the original data. By increasing the number, an image of a rigid articulated object that moves slower than the original rigid articulated object is generated, or conversely, by reducing the number of generated data, it moves faster than the original rigid articulated object For example, it is possible to generate an image of a rigid articulated object, and to easily edit the motion of the object.

Embodiment 12 FIG. In the eleventh embodiment, the expansion processing of the multidimensional time-series data is realized by software, but this data expansion processing may be realized by dedicated hardware. FIG. 28 shows a multi-dimensional time-series data decompression device in which the processing flow of FIG. 27 is made into a dedicated hardware. In the drawing, 200a is a multi-dimensional compressed data input means for inputting compressed Motion Data, and 61 is a compressed data. Means for decomposing the multidimensional time-series data into a plurality of compressed one-dimensional time-series data, 62
Is a one-dimensional time-series data decompression means for decompressing the decomposed one-dimensional time-series data using the same configuration as that of the decompression device of the sixth or eighth embodiment, and 63 is a series of one-dimensional time-series data. The determination means 200b for determining whether or not the expansion has been completed is output processing for outputting a series of expanded one-dimensional time-series data.

Next, the operation will be described. First, compressed Motion Data is input by the input means 200a. Next, the compressed Motion D
Ata is decomposed into one-dimensional compressed time-series data for each element, and an index number is given to each compressed one-dimensional time-series data.
The processing after this decomposing means 61 is the same as that of the one-dimensional time-series data decompression device of the sixth or eighth embodiment. That is, the one-dimensional time-series data decompression means 62 after the decomposing means 61 performs the processing in the sixth or eighth embodiment.
A decompression process is performed on each of the decomposed one-dimensional time-series data by the same decompression device.

When it is determined by the determining means 63 that all the one-dimensional time-series data has been decompressed, the output means 200b compresses the compressed one-dimensional time-series data, that is, the expanded multi-dimensional time-series data. Outputs dimensional Motion Data. As described above, according to the twelfth embodiment, the compressed multidimensional time-series data is decomposed into a plurality of one-dimensional time-series data, and the sixth embodiment is performed for each one-dimensional time-series data.
Alternatively, since the same decompression device as in the eighth embodiment is applied to perform decompression, the decompression processing can be performed at high speed even on multidimensional compressed time-series data using dedicated hardware.

When the data is expanded, the number of data to be generated can be set to a number different from the original data. In particular, when the Motion Data is expanded, the data to be generated is compared with the original data. By increasing the number, an image of a rigid articulated object that moves slower than the original rigid articulated object is generated, or conversely, by reducing the number of generated data, it operates faster than the original rigid articulated object For example, it is possible to generate an image of a rigid articulated object, and to easily edit the motion of the object.

[0212]

As described above, according to the method for compressing one-dimensional time-series data according to claim 1 of the present invention, a method for compressing one-dimensional time-series data at equal time intervals is provided. A first step of inputting data and an approximation accuracy thereof, a second step of calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data, and a third step of optimizing the position of the node candidate And a step of determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data based on the node candidate whose position has been optimized.
A fifth step of changing the number of nodes when it is determined in the fourth step that the error exceeds a value based on the approximation accuracy, and returning to the second step; A sixth step of outputting, as compressed information, the data of the node candidate and the data of the time corresponding to the node candidate when it is determined in the step that the error does not exceed the value based on the approximation accuracy. Therefore, compression can be performed in accordance with the properties of given one-dimensional time-series data, and the compression rate can be controlled by approximation accuracy, so that errors after decompression can be grasped in advance. The effect is obtained.

According to the one-dimensional time-series data compression method of the second aspect of the present invention, there is provided a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are A first step of inputting the one-dimensional time series; a second step of determining whether or not the one-dimensional time series data includes data within the approximation accuracy; Calculating a node candidate for an interpolation function that approximates the one-dimensional time-series data when it is determined that the data does not include data within the approximation accuracy;
And a fourth step of optimizing the position of the node candidate, and the one-dimensional time-series data and the original one-dimensional time-series data generated by the interpolation function based on the node candidate whose position has been optimized. A fifth step of determining an error of
A sixth step of changing the number of nodes and returning to the third step when it is determined that the error exceeds a value based on the approximation accuracy in the second step; When it is determined that the data includes data within the approximation accuracy, information that the one-dimensional time-series data is data within the approximation accuracy is output, and the error is reduced by the fifth step. The seventh step of outputting the data of the node candidate and the data of the corresponding time as compressed information when it is determined that the value does not exceed the value based on the approximation accuracy is given. Compression can be performed in accordance with the properties of the one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy. Process can be omitted, and the effect of time-series data compression method 1D is obtained.

According to a third aspect of the present invention, there is provided a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are obtained. And an index is added to the one-dimensional time-series data in the order of the time.
A first step of calculating the initial number of nodes of an interpolation function for interpolating the dimensional time-series data, and from the one-dimensional time-series data, always including start and end data, and randomly selecting only the number of the nodes. A second step of determining a nodal candidate, and a third step of interpolating the nodal candidate with an interpolation function using an index number as an independent variable to calculate an error from the original one-dimensional time-series data; A fourth step of calculating a value of a first objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance from the error, such that the value of the first objective function is minimized. A fifth step of repeatedly changing node candidates to determine a sub-optimal node candidate, and interpolating the sub-optimal node candidate by the interpolation function to obtain an original 1
A sixth step of generating one-dimensional time-series data that approximates the one-dimensional time-series data and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; A seventh step of calculating a value of the second objective function defined by weighted addition of the value, the error average, and the error variance;
If the value of the second objective function is equal to or greater than the threshold value corresponding to the approximation accuracy, the value obtained by adding an increment to the number of nodes is set as a new number of nodes, and the processing from the second step to the seventh step is repeated. Eighth step, if the value of the second objective function is less than the threshold, the initial time and time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the And a ninth step of outputting compressed data composed of the values
Since compression can be performed according to the properties of the dimensional time-series data and the compression ratio can be controlled by the approximation accuracy, there is an effect that a one-dimensional time-series data compression method can be obtained in which an error after expansion can be grasped in advance.

According to the one-dimensional time-series data compression method of the fourth aspect of the present invention, there is provided a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are And an index is added to the one-dimensional time-series data in the order of the time.
A first step of calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; and a step which always includes start and end data from the one-dimensional time-series data, and is approximately equal to the index. A second step of determining node candidates of only several nodes so as to form an interval; and interpolating the node candidates by an interpolation function using an index number as an independent variable to obtain an error from the original one-dimensional time-series data. A third step of calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance; and Repeatedly change the node candidates so that the value of the objective function is minimized,
A fifth step of determining a sub-optimal node candidate, and interpolating the sub-optimal node candidate by the interpolation function to generate one-dimensional time series data approximating the original one-dimensional time series data; A sixth step of calculating an error between the series data and the original one-dimensional time-series data; and, from the error, a second objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance. A seventh step of calculating a value;
If the value of the objective function is equal to or greater than the threshold value corresponding to the approximation accuracy, the value obtained by adding an increment to the number of nodes is set as a new number of nodes, and the processing from the second step to the seventh step is repeated. If the value of the second objective function is less than the threshold, the initial time and time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate Since the ninth step of outputting the composed compressed data is included, the compression can be performed in accordance with the property of the given one-dimensional time-series data, and the compression ratio can be controlled by the approximation accuracy. There is an effect that a one-dimensional time-series data compression method capable of grasping an error in advance can be obtained.

According to the one-dimensional time-series data compression method of the fifth aspect of the present invention, there is provided a method of compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are A first step of adding an index to the one-dimensional time-series data in the order of time and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; It is determined whether or not all the absolute values of the data are equal to or less than the approximation accuracy. If the absolute values are equal to or less than the approximation accuracy, an identifier indicating that they are all 0 is output, and the process is terminated. From the one-dimensional time-series data,
A third step of always including the start and end data and randomly determining only a few node candidates, and interpolating the node candidates by an interpolation function using an index number as an independent variable to obtain the original 1 A fourth step of calculating an error from the dimensional time-series data, and a first step defined by weighted addition of the maximum value of the error, the error average, and the error variance from the error.
A fifth step of calculating the value of the objective function, a sixth step of repeatedly changing node candidates so as to minimize the value of the first objective function, and determining a sub-optimal node candidate; A node candidate is interpolated by the interpolation function to generate one-dimensional time-series data approximating the original one-dimensional time-series data, and an error between the one-dimensional time-series data and the original one-dimensional time-series data is calculated. A step of calculating a value of a second objective function defined by weighted addition of a maximum value of the error, an error average, and an error variance from the error; and a value of the second objective function. Is greater than or equal to a threshold value corresponding to the approximation accuracy, a value obtained by adding an increment to the number of nodes is set as a new number of nodes, and a ninth step of repeating the processing from the third step to the eighth step is provided. If the value of the second objective function is less than the threshold, the one-dimensional Since the method includes the tenth step of outputting compressed data composed of the initial time and time interval of the sequence data, the index number of the finally determined node candidate, and the value of the node candidate, Compression can be performed according to the properties of the obtained one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy, so that errors after decompression can be grasped in advance, and the processing of data within approximation accuracy is omitted. There is an effect that a possible one-dimensional time-series data compression method can be obtained.

Further, according to the one-dimensional time-series data compression method of the present invention, there is provided a method for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are A first step of adding an index to the one-dimensional time-series data in the order of time and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; It is determined whether or not all the absolute values of the data are less than or equal to the approximation accuracy. If the absolute values are less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output and the process is terminated. And a second step of shifting from the one-dimensional time-series data, including only the start and end data, and selecting only a few node candidates so as to be approximately equally spaced with respect to the index. decide A third step, by interpolating the interpolation function for the index number as an independent variable the node candidates,
A fourth step of calculating an error from the original one-dimensional time-series data, and calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance A fifth step of repeatedly changing node candidates so that the value of the first objective function is minimized, and determining a sub-optimal node candidate; and Generating a one-dimensional time-series data approximating the original one-dimensional time-series data, and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; An eighth step of calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance; If above the corresponding threshold, add an increment to the number of nodes Things as a new number of nodes, the third
A ninth step of repeating the processing from the step to the eighth step, and if the value of the second objective function is less than the threshold value, the initial time and the time interval of the one-dimensional time-series data are finally determined. And a tenth step of outputting compressed data composed of the index numbers of the obtained node candidates and the values of the node candidates, so that the compression in accordance with the properties of the given one-dimensional time-series data can be performed. Since the compression ratio can be controlled by the approximation accuracy, an error after decompression can be grasped in advance, and there is an effect of obtaining a one-dimensional time-series data compression method that can omit the processing for data within the approximation accuracy. .

According to the one-dimensional time-series data compression method according to claim 7 of the present invention, in the one-dimensional time-series data compression method according to any one of claims 3 to 6, in the one-dimensional time-series data compression method, The calculation is based on the index of the node candidate, which is given by I (j), 0 ≦ j ≦ m, where I (j−1) <I (j) −1
Is satisfied, the node candidate I (j) is converted to the node candidate I (j) -1.
Calculates the value of the first objective function at the time of replacement, and subtracts the original value of the first objective function from the value of the first objective function, Δ
E (1-) is calculated, and if I (j-1) ≧ I (j) -1, ΔE (1-) is set to 0, and I (j) +1 <I (j + 1) If the relationship holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first first function is calculated from the value of the first objective function. Calculate the value ΔE (1+) by subtracting the value of the objective function,
If I (j) + 1 ≧ I (j + 1), the ΔE (1+) is set to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, The node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j ) Is replaced with the node candidate I (j) +1,
If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE
(1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I
(j) is replaced with the node candidate I (j) -1, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and the ΔE (1-)
Is larger than the ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 is performed in the order of small to large for odd j, and even j for odd j. Are performed in the order from the largest to the smallest, and if the value of the first objective function at the end of the series of processing is equal to or less than the value obtained by subtracting the threshold from the value of the original first objective function, the operation is performed in an odd number. J is performed again in ascending order from the smallest to the largest j, and for even j, the order is changed from the largest to the smallest, and whether the node candidates are not exchanged at all or the value of the first objective function is If the value is larger than the value obtained by subtracting the threshold value from the value of one objective function, the processing is terminated to perform the processing. Therefore, the processing for obtaining the sub-optimal node of the interpolation function can be realized, and the given one-dimensional time-series data Performing compression to match the properties, compression ratio because it can control the accuracy of approximation, one-dimensional time series data compression method that can recognizes in advance error after elongation is the effect obtained.

According to the one-dimensional time-series data compression method according to the eighth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, in the one-dimensional time-series data compression method, The calculation is based on the index of the node candidate, which is given by I (j), 0 ≦ j ≦ m, where I (j−1) <I (j) −1
Is satisfied, the node candidate I (j) is converted to the node candidate I (j) -1.
Calculates the value of the first objective function at the time of replacement, and subtracts the original value of the first objective function from the value of the first objective function, Δ
E (1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and I (j) +1 <I (j +1), the node candidate I (j) is replaced by the node candidate I (j) +1
The value of the first objective function at the time of replacement is calculated, a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) If the relationship of + 1 ≧ I (j + 1) holds, set ΔE (1+) to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, Node candidate
I (j) is replaced with the node candidate I (j) -1, and ΔE (1-) ≧ 0
And if the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the ΔE (1-) ≧
0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidates I (j) are not exchanged, and the relationships of ΔE (1-) <0 and ΔE (1 +) <0 hold. And, if the ΔE (1-) is not more than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and ΔE (1 +) <0
Holds, and ΔE (1-) is greater than ΔE
If it is larger than (1+), the operation of exchanging the node candidate I (j) with the node candidate I (j) +1 is performed in the order from the largest to the smallest for the odd j, and smaller for the even j. If the value of the first objective function at the end of the series of processes is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the above operation is performed for odd j. The order from the largest to the smallest one and the j of the even number are repeated again from the smallest to the largest one, and the exchange of the node candidates was not performed at all, or the value of the first objective function was changed to the value of the original first objective function. If the value is larger than the value obtained by subtracting the threshold value from the value, the process is terminated to terminate the process. Therefore, the process of obtaining the sub-optimal node of the interpolation function can be realized, and the process is performed according to the property of the given one-dimensional time-series data. Compression is performed, the compression ratio because it can control the accuracy of approximation, one-dimensional time series data compression method that can recognizes in advance error after elongation is the effect obtained.

According to the one-dimensional time-series data compression method of the ninth aspect of the present invention, in the one-dimensional time-series data compression method of any one of the third to sixth aspects, the quasi-optimal node candidate The calculation is performed by indexing the index of the node candidate in ascending order as I (j), 0 ≦ j ≦ m, where I (j−1) <I (j) −1
Is satisfied, the node candidate I (j) is converted to the node candidate I (j) -1.
The value of the first objective function at the time of replacement is calculated, and the value ΔE (1) obtained by subtracting the original value of the first objective function from the value of the first objective function is obtained.
-) Is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + 1) Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the first first objective function is calculated from the value of the first objective function. Value ΔE (1+) obtained by subtracting the value of the objective function
If the relationship of I (j) + 1 ≧ I (j + 1) holds, ΔE (1+) is set to 0, ΔE (1-) <0 and ΔE (1
+) ≧ 0, the node candidate I (j) is replaced with the node candidate I (j) -1, and the relationship ΔE (1-) ≧ 0 and ΔE (1 +) <0 is satisfied. Is satisfied, the node candidate I (j) is replaced with the node candidate I (j) + 1.If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 is satisfied, the node Candidate I
(j) is not exchanged, the ΔE (1-) <0 and the ΔE (1+)
<0, and ΔE (1-) is equal to ΔE (1
+) If below, the node candidate I (j) is replaced by the node candidate I (j)-
If the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is larger than the ΔE (1+), the node candidate The operation of exchanging I (j) for the node candidate I (j) +1 is performed in order from j = 1 to [m / 2] and from j = m-1 to [m / 2] +1. If the value of the first objective function at the time when the processing of the above is completed is equal to or less than the value obtained by subtracting the threshold from the value of the original first objective function, the operation is performed by j = 1
To [m / 2] and j = m-1 to [m / 2] +1 again, and whether the exchange of the node candidates has not been performed at all or the value of the first objective function is the original If the value is larger than the value obtained by subtracting the threshold value from the value of the first objective function, the processing is terminated to perform the processing. Therefore, the processing for obtaining the sub-optimal node of the interpolation function can be realized, and the given one-dimensional time series is obtained. Since compression can be performed in accordance with the characteristics of data and the compression ratio can be controlled by approximation accuracy, there is an effect that a one-dimensional time-series data compression method can be obtained in which errors after decompression can be grasped in advance.

According to the one-dimensional time-series data compression method according to the tenth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects,
The calculation of the quasi-optimal node candidate is as follows: when the index of the node candidate is numbered in ascending order and expressed as I (j), 0 ≦ j ≦ m, I (j−1) < I (j)-
If the relation of 1 holds, the node candidate I (j) is replaced with the node candidate I (j).
Calculate the value of the first objective function when the value is changed to -1, and
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + If the relationship of 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original is calculated from the value of the first objective function. The value ΔE (1
+), And if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0 and the Δ
If the relationship of E (1+) ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, the ΔE (1-) ≧ 0 and the ΔE (1 +) < If the relation of 0 holds, the node candidate I (j)
Is replaced by the node candidate I (j) +1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate
Without the exchange of I (j), ΔE (1-) <0 and ΔE (1
+) <0, and ΔE (1-) is equal to ΔE (1
+) If below, the node candidate I (j) is replaced by the node candidate I (j)-
If the relation of ΔE (1-) <0 and the relation of ΔE (1 +) <0 hold, and the ΔE (1-) is larger than the ΔE (1+), the node candidate I The operations for exchanging (j) for the node candidate I (j) +1 are from j = [m / 2] to 1, and j = [m / 2]
+1 to m−1 in order, and if the value of the first objective function at the time when these series of processes are completed is equal to or less than the value of the original first objective function minus the threshold, the operation is performed by j = [M /
2] to 1 and j = [m / 2] +1 to m−1 again, and the exchange of the node candidates was not performed at all, or the value of the first objective function was changed to the original first value. If the value is larger than the value obtained by subtracting the threshold value from the value of the objective function, the process is terminated, so that the process for obtaining a sub-optimal node of the interpolation function can be realized. Since compression according to the characteristics can be performed and the compression ratio can be controlled by approximation accuracy, there is an effect that a one-dimensional time-series data compression method can be obtained in which an error after decompression can be grasped in advance.

According to the one-dimensional time-series data compression method of the present invention, in the one-dimensional time-series data compression method of any one of the third to sixth aspects,
The calculation of the quasi-optimal node candidate is as follows: when the index of the node candidate is numbered in ascending order and expressed as I (j), 0 ≦ j ≦ m, I (j−1) < I (j)-
If the relation of 1 holds, the node candidate I (j) is replaced with the node candidate I (j).
Calculate the value of the first objective function when the value is changed to -1, and
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + If the relationship of 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original is calculated from the value of the first objective function. The value ΔE (1
+), And if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0 and the Δ
If the relationship of E (1+) ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, the ΔE (1-) ≧ 0 and the ΔE (1 +) < If the relation of 0 holds, the node candidate I (j)
Is replaced by the node candidate I (j) +1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate
Without the exchange of I (j), ΔE (1-) <0 and ΔE (1
+) <0, and ΔE (1-) is equal to ΔE (1
+) If below, the node candidate I (j) is replaced by the node candidate I (j)-
If the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1 in order from j = 1 to m−1, and the value of the first objective function at the time when these series of processing is completed is equal to the original first value.
If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the objective function, the above operation is performed again in order from j = 1 to m−1, and the exchange of the node candidates was not performed at all, or the value of the first objective function was If the value is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, the process is terminated to terminate the process. Therefore, the process of obtaining the sub-optimal node of the interpolation function can be realized, and the given one-dimensional node can be realized. Since compression can be performed in accordance with the properties of time-series data and the compression ratio can be controlled by approximation accuracy, there is an effect that a one-dimensional time-series data compression method can be obtained in which errors after decompression can be grasped in advance.

According to the one-dimensional time-series data compression method according to the twelfth aspect of the present invention, in the one-dimensional time-series data compression method according to any one of the third to sixth aspects, the calculation of the sub-optimal node candidate is performed. Is expressed as I (j), 0 ≦ j ≦ m with respect to the indices of the node candidates in ascending order, and I (j−1) <I (j) −1
Is satisfied, the node candidate I (j) is converted to the node candidate I (j) -1.
The value of the first objective function at the time of replacement is calculated, and the value ΔE (1) obtained by subtracting the original value of the first objective function from the value of the first objective function is obtained.
-) Is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + 1) Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the first first objective function is calculated from the value of the first objective function. Value ΔE (1+) obtained by subtracting the value of the objective function
If the relationship of I (j) + 1 ≧ I (j + 1) holds, ΔE (1+) is set to 0, ΔE (1-) <0 and ΔE (1
+) ≧ 0, the node candidate I (j) is replaced with the node candidate I (j) -1, and the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 is satisfied. Is satisfied, the node candidate I (j) is replaced with the node candidate I (j) + 1.If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 is satisfied, the node Candidate I
(j) is not exchanged, the ΔE (1-) <0 and the ΔE (1+)
<0, and the ΔE (1-) is the ΔE (1+)
If below, the node candidate I (j) is replaced by the node candidate I (j) -1.
When the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold and the ΔE (1-) is larger than the ΔE (1+), the node candidate I ( The operation of exchanging j) for the node candidate I (j) +1 is performed in order from j = m-1 to 1, and the value of the first objective function at the time when a series of these processes is completed is changed to the original first objective. If the value is equal to or less than the value obtained by subtracting the threshold from the value of the function, the above operation is performed again from j = m-1 to 1 in order, and whether the exchange of the node candidates has not been performed at all or the value of the first objective function is the original If the value is larger than the value obtained by subtracting the threshold value from the value of the first objective function, the process is terminated to terminate the process. Therefore, the process of obtaining a sub-optimal node of the interpolation function can be realized. Compression can be performed according to the characteristics of the series data, and the compression ratio can be controlled by approximation accuracy, so that errors after decompression are known in advance The effect of time-series data compression method 1D, which may Rukoto is obtained.

According to the one-dimensional time-series data compression method according to the thirteenth aspect of the present invention, the one-dimensional time-series data compression method according to any one of the third to sixth aspects,
The calculation of the quasi-optimal node candidate is as follows: when the index of the node candidate is numbered in ascending order, I (j), 0 ≦ j ≦ m, I (j−1) < I (j)
If the relation of -1 holds, the node candidate I (j) is replaced with the node candidate I (j).
Calculate the value of the first objective function when the value is changed to -1, and
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + If the relationship of 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original is calculated from the value of the first objective function. The value ΔE (1
+), And if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0 and the Δ
If the relationship of E (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of this exchange and the element The value of the first objective function is exchanged, and if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1 +) <0 hold, the node candidate I (j) is replaced with the node candidate
I (j) +1 and the value of the first objective function at the time of this exchange and the value of the original first objective function are exchanged to obtain ΔE (1-) ≧ 0 and ΔE ( If the relationship of 1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE ( 1-) is equal to or less than the ΔE (1+), the node candidate I
(j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of this exchange and the value of the original first objective function are exchanged. ) <0 and the ΔE (1 +) <
0 holds, and the ΔE (1-) is the ΔE (1+)
If greater, the node candidate I (j) is replaced with the node candidate I
(j) +1 and the operation of exchanging the value of the first objective function and the value of the original first objective function at the time of this exchange is performed for odd j, from small to large. The order and the even j are performed in ascending order from the largest to the smallest. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, The above operation is performed again in the order of small to large for the odd j, and in the order of large to small for the even j.
If the value of the objective function is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the process is terminated, thereby performing the process of obtaining the sub-optimal node of the interpolation function. The compression can be performed in accordance with the properties of the given one-dimensional time-series data, and the compression ratio can be controlled by the approximation accuracy. There is.

According to the one-dimensional time-series data compression method according to the fourteenth aspect of the present invention, the one-dimensional time-series data compression method according to any one of the third to sixth aspects,
The calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order.
When I (j), 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j) is changed to the node candidate I (j) -1. The value of the first objective function at the time of replacement is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function
If the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is established. Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Is calculated by subtracting the value of ΔE (1+), and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the above Δ
E (1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship of ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of this exchange and the original first objective function are Exchange values, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, replace the node candidate I (j) with the node candidate I (j) +1 The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the ΔE
If (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0
And the relationship of ΔE (1 +) <0 holds, and ΔE (1+
-) Is equal to or less than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original If the values of the first objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is greater than the ΔE (1+) For example, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the exchange of the value of the first objective function and the value of the original first objective function at the time of the exchange is performed. The operation to be performed is performed in the order of large to small for the odd j, and in the order of small to large for the even j, and the value of the first objective function when the series of processes is completed is changed to the original first value. If the value of the objective function is equal to or less than the value obtained by subtracting the threshold value, the above operation is performed in the order of large to small for odd j, and for even j. The process is performed again from the largest to the smallest, and if the exchange of the node candidates has not been performed at all or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is performed. , The processing for obtaining the sub-optimal node of the interpolation function can be realized, the compression can be performed in accordance with the property of the given one-dimensional time-series data, and the compression ratio can be determined by the approximation accuracy. Since control is possible, there is an effect that a one-dimensional time-series data compression method can be obtained in which an error after decompression can be grasped in advance.

According to the one-dimensional time-series data compression method of the present invention, in the one-dimensional time-series data compression method of any one of claims 3 to 6,
The calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order.
When I (j), 0 ≤ j ≤ m, if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j) is changed to the node candidate I (j) -1. The value of the first objective function at the time of replacement is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function
If the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is established. Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Is calculated by subtracting the value of ΔE (1 +). If the relationship of I (j) + 1 ≧ I (j + 1) holds,
(1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original first objective function are Exchange values, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, exchange the node candidate I (j) with the node candidate I (j) +1 The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the ΔE
If (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0
And the relationship of ΔE (1 +) <0 holds, and ΔE (1+
-) Is equal to or less than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original If the values of the first objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is greater than the ΔE (1+), For example, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the exchange of the value of the first objective function and the value of the original first objective function at the time of the exchange is performed. J = 1
To [m / 2], and from j = m-1 to [m / 2] +1, and the value of the first objective function at the end of the series of processes is the value of the original first objective function. If the value is equal to or less than the value obtained by subtracting the threshold from the value, the above operation is performed again from j = 1 to [m / 2] and from j = m-1 to [m / 2] +1 again, and the exchange of the node candidates is performed. If not performed, or if the value of the first objective function is greater than the value of the original first objective function minus the threshold, the decision is made by terminating the process. A process for finding a suboptimal node of a function can be realized, compression can be performed according to the properties of given one-dimensional time-series data, and a compression ratio can be controlled by approximation accuracy, so that errors after decompression can be grasped in advance. There is an effect that a one-dimensional time-series data compression method can be obtained.

According to the one-dimensional time-series data compression method of the present invention, in the one-dimensional time-series data compression method of any one of claims 3 to 6,
The calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order.
When I (j), 0 ≤ j ≤ m, if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j) is changed to the node candidate I (j) -1. The value of the first objective function at the time of replacement is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function
If the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is established. Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Is calculated by subtracting the value of ΔE (1 +). If the relationship of I (j) + 1 ≧ I (j + 1) holds,
(1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original first objective function are Exchange values, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, exchange the node candidate I (j) with the node candidate I (j) +1 The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the ΔE
If (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0
And the relationship of ΔE (1 +) <0 holds, and ΔE (1+
If-) is equal to or smaller than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original If the values of the first objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is greater than the ΔE (1+), For example, an operation of exchanging the node candidate I (j) with the node candidate I (j) +1 and exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange. To j = [m / 2
] To 1 and j = [m / 2] +1 to m-1 in order, and the value of the first objective function at the time when these series of processing is completed is determined by the threshold value from the value of the original first objective function. If not more than j = [m / 2] to 1, and
j = [m / 2] +1 to m−1 again in order, and the exchange of the node candidates is not performed at all, or the value of the first objective function is set to a threshold value from the value of the original first objective function. If it is larger than the reduced one, the processing is terminated to terminate the processing, so that processing for obtaining a sub-optimal node of the interpolation function can be realized, and compression can be performed according to the properties of the given one-dimensional time-series data. Since the compression ratio can be controlled by the approximation accuracy, there is an effect that a one-dimensional time-series data compression method can be obtained in which an error after decompression can be grasped in advance.

According to the one-dimensional time-series data compression method of the present invention, in the one-dimensional time-series data compression method according to any one of claims 3 to 6,
The calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order.
When I (j), 0 ≤ j ≤ m, if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j) is changed to the node candidate I (j) -1. The value of the first objective function at the time of replacement is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function
If the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is established. Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Is calculated by subtracting the value of ΔE (1 +). If the relationship of I (j) + 1 ≧ I (j + 1) holds,
(1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original first objective function are Exchange values, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, exchange the node candidate I (j) with the node candidate I (j) +1 The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the ΔE
If (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0
And the relationship of ΔE (1 +) <0 holds, and ΔE (1+
-) Is equal to or less than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original If the values of the first objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is greater than the ΔE (1+), For example, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the exchange of the value of the first objective function and the value of the original first objective function at the time of the exchange is performed. J = 1
To m−1, and if the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the above operation is performed from j = 1. m-1
Until the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is terminated. , The processing for obtaining the sub-optimal node of the interpolation function can be realized, the compression can be performed according to the property of the given one-dimensional time series data, and the compression ratio can be controlled by the approximation accuracy. There is an effect that a one-dimensional time-series data compression method can be obtained in which the error of (1) can be grasped in advance.

According to the one-dimensional time-series data compression method of the eighteenth aspect of the present invention, in the one-dimensional time-series data compression method of any one of the third to sixth aspects,
The calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order.
When I (j), 0 ≤ j ≤ m, if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j) is changed to the node candidate I (j) -1. The value of the first objective function at the time of replacement is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function
If the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and the relationship of I (j) +1 <I (j + 1) is established. Is satisfied, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the original first objective function is calculated from the value of the first objective function. Is calculated by subtracting the value of ΔE (1 +). If the relationship of I (j) + 1 ≧ I (j + 1) holds,
(1+) is set to 0, ΔE (1-) <0 and ΔE (1+)
If the relationship ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original first objective function are Exchange values, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, exchange the node candidate I (j) with the node candidate I (j) +1 The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the ΔE
If (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0
And the relationship of ΔE (1 +) <0 holds, and ΔE (1+
If-) is equal to or smaller than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original If the values of the first objective function are exchanged and the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 hold, and the ΔE (1-) is greater than the ΔE (1+), For example, the node candidate I (j) is replaced with the node candidate I (j) +1, and the exchange of the value of the first objective function and the value of the original first objective function at the time of the exchange is performed. J = m-
Steps from 1 to 1 are performed in order. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operation is performed by j = m-1 From 1
Until the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is terminated. , The processing for obtaining the sub-optimal node of the interpolation function can be realized, the compression can be performed according to the property of the given one-dimensional time series data, and the compression ratio can be controlled by the approximation accuracy. There is an effect that a one-dimensional time-series data compression method can be obtained in which the error of (1) can be grasped in advance.

According to the one-dimensional time-series data compression method according to the nineteenth aspect of the present invention, the one-dimensional time-series data compression method according to any one of the third to sixth aspects,
If the finally determined number of node candidates is equal to or less than the number of data that is not a candidate, the identifier indicating the node candidate, the index number of the finally determined node candidate, and the value of the node candidate are used. Outputting the composed compressed data, if the finally determined number of node candidates is larger than the number of data that did not become the candidate, an identifier that is not a node candidate and an index of the data that did not become the node candidate Since the compressed data composed of the numbers and the values of the node candidates is output, the compression can be performed according to the properties of the given one-dimensional time-series data, and the compression ratio can be controlled by the approximation accuracy. There is an effect that a one-dimensional time-series data compression method capable of grasping later errors in advance can be obtained.

According to the one-dimensional time-series data compression method of the present invention, in the one-dimensional time-series data compression method according to any one of the first to sixth aspects,
For one-dimensional time-series data with unequal intervals in time, the one-dimensional time-series data compression method is applied independently to time and data, and each is compressed independently. Even for spaced one-dimensional time-series data, compression can be performed in accordance with the properties of the given one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy, so that errors after decompression can be grasped in advance. There is an effect that a one-dimensional time-series data compression method can be obtained.

According to the one-dimensional time-series data compression method of the present invention, in the one-dimensional time-series data compression method of any one of the first to sixth aspects,
By repeatedly applying the one-dimensional time-series data compression method to each of a plurality of one-dimensional time-series data constituting the multi-dimensional time-series data, the multi-dimensional time-series data is compressed. For dimensional time series data,
Compression can be performed according to the properties of each one-dimensional time series data that constitutes given multi-dimensional time series data, and the compression ratio can be controlled by approximation accuracy, so that errors after decompression can be grasped in advance There is an effect that a sequence data compression method can be obtained.

According to the one-dimensional time-series data compression method of the present invention, in the one-dimensional time-series data compression method according to any one of the first to sixth aspects,
For one-dimensional time-series data in which a plurality of errors propagate, the approximation accuracy value is increased in order from the one-dimensional time-series data of the propagation source, and the one-dimensional time-series data compression method is repeatedly applied. Since the one-dimensional time-series data is compressed, the compression can be performed in accordance with the properties of the given one-dimensional time-series data without increasing the propagation of error, and the compression ratio can be controlled by approximation accuracy. In addition, there is an effect that a one-dimensional time-series data compression method can be obtained in which an error after decompression can be grasped in advance.

According to the one-dimensional time-series data decompression method according to the twenty-third aspect of the present invention,
A method for expanding compressed data compressed by the one-dimensional time-series data compression method according to any one of the above, wherein a first step of inputting the compressed data and the number of data when the compressed data is expanded; By interpolating the compressed data using the same interpolation function as that used in the compression, the same number of data as the number of data is calculated, and the time is calculated from the initial time and the time interval by the same number as the number of data. Only, and the third step of outputting the data and the time calculated in the second step is included, so that the continuity using the interpolation function is also used for the decompression. A one-dimensional time-series data decompression method capable of decompressing the compressed data compressed by the one-dimensional time-series data compression method according to any one of claims 1, 3 and 4, and decompressing an arbitrary number of data. Is obtained There is a result.

Further, according to the one-dimensional time series data decompression method according to claim 24 of the present invention, claim 2, 5 or 6
A method for expanding compressed data compressed by the one-dimensional time-series data compression method according to any one of the above, wherein a first step of inputting the compressed data and the number of data when the compressed data is expanded; When an identifier indicating that all the data is 0 is given to the compressed data, the time is calculated from the initial time and the time interval by the same number of 0s as the number of data, and 0 as the number of data. In the case where the compressed data is not provided with an identifier indicating that the data is all 0, the compressed data is interpolated using the same interpolation function as the interpolation function used in the compression. A second step of calculating the same number of data as the number and calculating the time from the initial time and the time interval by the same number as the data number; and outputting the data and the time calculated in the second step. The third step and Since to include, with respect to extension, for using the serialized by the interpolation function, claim 2,5
Or a one-dimensional time-series data decompression method capable of decompressing the compressed data compressed by the one-dimensional time-series data compression method according to any one of (6) and (4), and decompressing an arbitrary number of data. .

According to the one-dimensional time series data decompression method of the twenty-fifth aspect of the present invention, the twenty-third or the twenty-fourth aspect of the present invention.
In the one-dimensional time-series data decompression method described above, the one-dimensional time-series data decompression method is repeatedly applied to each of a plurality of compressed one-dimensional time-series data constituting the compressed multi-dimensional time-series data. Since the compressed multi-dimensional time-series data is expanded, the one-dimensional time-series data expansion method according to claim 23 or 24 is applied to the compressed data of the multi-dimensional time-series data. There is an effect that a one-dimensional time-series data decompression method that can decompress data in each dimension and decompress data in an arbitrary number is obtained.

According to the one-dimensional time-series data compression program recording medium of the twenty-sixth aspect of the present invention, there is provided a medium for recording a one-dimensional time-series data compression program at a time equal interval, wherein the one-dimensional time-series data compression program is recorded. A first step of inputting sequence data and its approximation accuracy, a second step of calculating node candidates for an interpolation function that approximates the one-dimensional time-series data, and a third step of optimizing the positions of the node candidates And a fourth step of determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data based on the node candidates whose positions have been optimized; and A fifth step of returning to the second step when it is determined by the step that the error exceeds a value based on the approximation accuracy, and the error does not exceed a value based on the approximation accuracy by the fifth step. Judged In this case, a one-dimensional time-series data compression program including a sixth step of outputting the data of the node candidate and the data of the time corresponding thereto as compressed information is recorded. One-dimensional time-series data compression program recording media that records programs can perform compression according to the properties of one-dimensional time-series data and control the compression ratio with approximation accuracy, so that errors after decompression can be grasped in advance. There is an effect that can be obtained.

According to a one-dimensional time-series data compression program recording medium according to claim 27 of the present invention, there is provided a medium recording a one-dimensional time-series data compression program at equal time intervals, comprising: A first step of inputting series data and its approximation accuracy, a second step of determining whether or not the one-dimensional time-series data includes data within the approximation accuracy, and the second step A third step of calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data when it is determined that the one-dimensional time-series data does not include data within the approximation accuracy; A fourth step of optimizing the position of the candidate, and determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data based on the node candidate whose position has been optimized. A step of returning to the third step when it is determined by the fifth step that the error exceeds a value based on the approximation accuracy; and a step of returning to the one-dimensional time by the second step. When it is determined that the data within the approximation accuracy is included in the series data, information that the one-dimensional time-series data is data within the approximation accuracy is output, and the error is reduced by the fifth step. A seventh step of outputting the node candidate data and the corresponding time data as compressed information when it is determined that the value does not exceed the value based on the approximation accuracy. Because the program is recorded, compression can be performed according to the properties of given one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy, so that errors after decompression can be grasped in advance. Can, the effect of one-dimensional time series data compression program recording medium recording a program can be obtained.

According to a one-dimensional time-series data compression program recording medium according to claim 28 of the present invention, there is provided a medium recording a time-equally-spaced one-dimensional time-series data compression program, wherein the one-dimensional time-series data compression program is recorded. A first step of inputting sequence data and its approximation accuracy, adding an index to the one-dimensional time-series data in the order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data. A second step of determining the node candidates of only a few nodes, which always includes the beginning and end data from the one-dimensional time-series data, and independently determining the index numbers of the node candidates. A third step of calculating an error with respect to the original one-dimensional time-series data by interpolating using an interpolation function as a variable; A fourth step of calculating the value of the first objective function defined by the addition and repeating the change of the node candidate so that the value of the first objective function is minimized, and determining the sub-optimal node candidate. And generating the one-dimensional time-series data approximating the original one-dimensional time-series data by interpolating the sub-optimal node candidates using the interpolation function. A sixth step of calculating an error with respect to the data, and a second step defined by weighted addition of the maximum value of the error, the average of the error, and the error variance from the error.
A seventh step of calculating a value of the objective function, and if the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy, a value obtained by adding an increment to the number of nodes is set as a new number of nodes; An eighth step of repeating the processing from the second step to the seventh step, and if the value of the second objective function is less than the threshold, the initial time and the time interval of the one-dimensional time-series data, A one-dimensional time-series data compression program including a ninth step of outputting compressed data composed of the index number of the determined node candidate and the value of the node candidate is recorded. One-dimensional time-series data compression programs that record programs can be compressed according to the properties of one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy, so that errors after decompression can be grasped in advance. The effect of the recording medium is obtained.

According to a one-dimensional time-series data compression program recording medium according to claim 29 of the present invention, there is provided a medium recording a time-equally-spaced one-dimensional time-series data compression program, comprising: A first step of inputting sequence data and its approximation accuracy, adding an index to the one-dimensional time-series data in the order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data. And a second step of determining, from the one-dimensional time-series data, node candidates of only a few nodes so as to always include start and end data and to be approximately equally spaced with respect to the index. And interpolating the node candidate by an interpolation function using the index number as an independent variable,
A third step of calculating an error from the dimensional time-series data; and a fourth step of calculating a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance from the error. And a fifth step of repeatedly changing node candidates so as to minimize the value of the first objective function to determine a sub-optimal node candidate, and interpolating the sub-optimal node candidate by the interpolation function. Then, one-dimensional time-series data that approximates the original one-dimensional time-series data is generated, and an error between the one-dimensional time-series data and the original one-dimensional time-series data is calculated.
And a seventh step of calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance. If the threshold value is equal to or greater than the threshold value corresponding to the approximation accuracy, a value obtained by adding an increment to the number of nodes is set as a new number of nodes, and an eighth step of repeating the processing from the second step to the seventh step; (2) If the value of the objective function is less than the threshold value, the compressed data composed of the initial time and time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate And a ninth step of outputting the one-dimensional time-series data compression program, so that the compression can be performed in accordance with the properties of the given one-dimensional time-series data, and the compression ratio can be controlled by the approximation accuracy. Because After the can recognizes in advance the error, the program has the effect of time-series data compression program recording medium 1 dimensional recorded is obtained a.

According to a one-dimensional time-series data compression program recording medium according to claim 30 of the present invention, there is provided a medium in which a one-dimensional time-series data compression program at an equal time interval is recorded, wherein the one-dimensional time-series data compression program is recorded. And a first step of inputting an approximation accuracy thereof, adding an index to the one-dimensional time-series data in order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data, 1
It is determined whether or not all the absolute values of the dimensional time-series data are less than or equal to the approximation accuracy. If the absolute value is less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output and the process is terminated. A second step of shifting to the third step, and a third step of randomly determining only a few node candidates including the start and end data from the one-dimensional time-series data. And interpolating the node candidate by an interpolation function using the index number as an independent variable,
A fourth step of calculating an error from the dimensional time-series data; and a fifth step of calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance. And a sixth step of repeatedly changing node candidates so as to minimize the value of the first objective function to determine a sub-optimal node candidate, and interpolating the sub-optimal node candidate by the interpolation function. A seventh step of generating one-dimensional time-series data approximating the original one-dimensional time-series data and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; An eighth step of calculating a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance, wherein the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy. Then, add the increment to the number of nodes A ninth step of repeating the processing from the third step to the eighth step, and an initial time of the one-dimensional time-series data if the value of the second objective function is less than the threshold. A tenth step of outputting compressed data composed of the time interval, the index number of the finally determined node candidate, and the value of the node candidate
Because a one-dimensional time-series data compression program is recorded, compression can be performed in accordance with the properties of given one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy. In addition, there is an effect that a one-dimensional time-series data compression program recording medium in which a program capable of omitting the processing for data within the approximation accuracy can be obtained.

According to the one-dimensional time-series data compression program recording medium of claim 31 of the present invention, there is provided a medium recording a one-dimensional time-series data compression program at equal time intervals, comprising: A first step of inputting sequence data and its approximation accuracy, adding an index to the one-dimensional time-series data in order of time, and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; ,
It is determined whether or not all the absolute values of the one-dimensional time-series data are less than or equal to the approximation accuracy.
A second step of outputting an identifier indicating that the processing is terminated, and otherwise, proceeding to a third step described below;
A third step of, among the one-dimensional time-series data, always including the start and end data and determining only a few node candidates so as to be approximately equally spaced with respect to the index; A fourth step of interpolating the node candidates by an interpolation function using an index number as an independent variable to calculate an error from the original one-dimensional time-series data; and, from the error, a maximum value of the error, an error average, and an error. A fifth step of calculating the value of the first objective function defined by the weighted addition with the variance, and repeatedly changing the node candidates so that the value of the first objective function is minimized; A sixth step of determining, and interpolating the sub-optimal node candidates using the interpolation function to generate one-dimensional time-series data approximating the original one-dimensional time-series data; One-dimensional time series data A seventh step of calculating an error from the data, and an eighth step of calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance. If the value of the second objective function is equal to or larger than the threshold value corresponding to the approximation accuracy, the number obtained by adding an increment to the number of nodes is set as a new number of nodes, and the processing from the third step to the eighth step is performed. Repeating the ninth step and the second step
If the value of the objective function is less than the threshold, the compressed data composed of the initial time and the time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate Since the one-dimensional time-series data compression program including the tenth step to output is recorded, compression can be performed according to the properties of the given one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy. In addition, there is an effect that a one-dimensional time-series data compression program recording medium which records a program which can grasp the error after decompression in advance and which can omit the processing for data within the approximation accuracy can be obtained.

According to the one-dimensional time-series data compression program recording medium of claim 32 of the present invention, in the one-dimensional time-series data compression program recording medium of any one of claims 28 to 31, The calculation of the optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j ≦ m.
When the relationship of I (j-1) <I (j) -1 holds, the first objective function of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) -1 Calculating a value, and calculating a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function,
If I (j-1) ≧ I (j) -1, the ΔE (1-) is set to 0, and I (j)
If the relationship of +1 <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the objective function is calculated. If I (j) + 1 ≧ I (j + 1), the value ΔE (1+) is set to 0. If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I
(j) is replaced with the node candidate I (j) -1, and ΔE (1-) ≧ 0
And if the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the ΔE (1-) ≧
0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed, and the relationships of ΔE (1-) <0 and ΔE (1 +) <0 hold. And if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I (j) is replaced with the node candidate
I (j) -1 and if the relationship of the above ΔE (1-) <0 and the above ΔE (1 +) <0 holds, and if the above ΔE (1-) is larger than the above ΔE (1+) The node candidate I (j) is replaced with the node candidate I (j) +1
Are performed in order from small to large for odd j, and from large to small for even j, and the value of the first objective function at the time when these series of processing is completed is changed to the original value. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the first objective function, the operation is performed using an odd number.
j is performed in ascending order from the smallest to the largest, and for even j, the order is changed from the largest to the smallest, and whether the node candidates are not exchanged at all or the value of the first objective function is equal to the original first value. If the value is larger than the value obtained by subtracting the threshold value from the value of the objective function, the program to be executed is recorded by terminating the process, so that the process of obtaining the sub-optimal node of the interpolation function can be realized.
One-dimensional time-series data compression program recording that records a program that can perform compression according to the properties of given one-dimensional time-series data and can control the compression ratio by approximation accuracy, so that errors after decompression can be grasped in advance. There is an effect that a medium can be obtained.

According to the one-dimensional time-series data compression program recording medium of claim 33 of the present invention, in the one-dimensional time-series data compression program recording medium of any one of claims 28 to 31, The calculation of the optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j ≦ m.
When the relationship of I (j-1) <I (j) -1 holds, the first objective function of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) -1 Calculating a value, and calculating a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function,
If the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-)
Is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the first object when the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the function is calculated, and a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I (j + 1) If the relationship holds, then ΔE (1
+) Is set to 0, and ΔE (1-) <0 and ΔE (1+) ≧ 0
If the relationship holds, the node candidate I (j) is replaced with the node candidate I (j) -1, the ΔE (1-) ≧ 0 and the ΔE (1 +) <
0, the node candidate I (j) is replaced with the node candidate I (j) +1, and ΔE (1-) ≧ 0 and ΔE (1
+) ≧ 0 holds, the node candidate I (j) is not exchanged, the relations ΔE (1-) <0 and ΔE (1 +) <0 hold, and the ΔE ( If 1−) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) −1, the ΔE (1-) <0 and the ΔE (1+) <0, and if ΔE (1-) is greater than ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 Are performed in the order of large to small for odd j, and in the order of small to large for even j, and the value of the first objective function at the time when a series of these processes is completed is equal to the original first objective function. If the threshold value is less than the value obtained by subtracting the threshold value from the above value, the above operation is performed again in the order of large to small for odd j and in the order of small to large for even j, and Whether the replacement of the complement was not performed at all,
If the value of the objective function is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the program to be executed is recorded by terminating the process, so that a sub-optimal node of the interpolation function is obtained. Processing can be realized, compression can be performed according to the properties of given one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy. There is an effect that a series data compression program recording medium can be obtained.

According to the one-dimensional time-series data compression program recording medium of claim 34 of the present invention, in the one-dimensional time-series data compression program recording medium of any one of claims 28 to 31, The calculation of the optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j ≦ m.
If the relation I (j-1) <I (j) -1 holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) -1 Is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j−
1) If the relationship of ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+) and I (j) + 1 ≧
If the relationship of I (j + 1) holds, the ΔE (1+) is set to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is replaced by the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). Exchange to the node candidate I (j) +1, if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, do not exchange the node candidate I (j),
The relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1
-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I The operation of exchanging for (j) +1 is performed in order from j = 1 to [m / 2], and from j = m-1 to [m / 2] +1. If the value of the objective function is equal to or less than the value of the original first objective function minus the threshold, the operation is performed from j = 1 to [m / 2] and j = m-1 to [m / 2]. +1) in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold, the process is performed. By ending, the program to be executed is recorded, so that processing for obtaining a sub-optimal node of the interpolation function can be realized, compression can be performed in accordance with the properties of given one-dimensional time-series data, and compression can be performed. Since the rate can be controlled by the approximation accuracy, one-dimensional time series data compression program storage medium storing a program capable recognizes in advance error after elongation is the effect obtained.

According to the one-dimensional time-series data compression program recording medium of claim 35 of the present invention, in the one-dimensional time-series data compression program recording medium of any one of claims 28 to 31, The calculation of the optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j ≦ m.
If the relation of I (j-1) <I (j) -1 holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) -1 Is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j−
1) If the relationship of ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+) and I (j) + 1 ≧
If the relationship of I (j + 1) holds, the ΔE (1+) is set to 0.If the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is replaced by the node candidate I (j). Exchange to the node candidate I (j) +1, if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, do not exchange the node candidate I (j),
The relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds,
And if ΔE (1-) is equal to or smaller than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is greater than ΔE (1+), the node candidate I
The operation of exchanging (j) for the node candidate I (j) +1 is j = [m / 2]
To 1 and j = [m / 2] +1 to m−1, and the value of the first objective function when these series of processes are completed is calculated from the value of the original first objective function by the threshold value. If not more than j = [m / 2] to 1, and
j = [m / 2] +1 to m−1 again in order, and whether the node candidates have not been exchanged at all or the value of the first objective function is set to a threshold value from the value of the original first objective function If it is larger than the subtracted one, the program to be executed is recorded by terminating the processing, so that the processing for obtaining the sub-optimal node of the interpolation function can be realized, and the processing can be performed according to the properties of the given one-dimensional time-series data. In addition, since the compression rate can be controlled and the compression ratio can be controlled by the approximation accuracy, a program which can grasp the error after decompression in advance is recorded.
There is an effect that a dimensional time series data compression program recording medium can be obtained.

According to a one-dimensional time-series data compression program recording medium according to claim 36 of the present invention, in the one-dimensional time-series data compression program recording medium according to any one of claims 28 to 31, The calculation of the optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j ≦ m.
If the relation of I (j-1) <I (j) -1 holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) -1 Is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j−
1) If the relationship of ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+) and I (j) + 1 ≧
If the relationship of I (j + 1) holds, the ΔE (1+) is set to 0.If the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is replaced by the node candidate I (j). Exchange to the node candidate I (j) +1, if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, do not exchange the node candidate I (j),
The relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds,
And if ΔE (1-) is equal to or smaller than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is greater than ΔE (1+), the node candidate I
The operation of replacing (j) with the node candidate I (j) +1 is from j = 1 to m-1
If the value of the first objective function at the end of the series of processes is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the above operation is performed from j = 1 to m-1. Repeatedly in order, if the exchange of node candidates has not been performed at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold, the process is terminated. Since the program to be executed is recorded, it is possible to realize processing for obtaining a sub-optimal node of the interpolation function, perform compression according to the properties of given one-dimensional time-series data, and control the compression ratio by approximation accuracy. In addition, there is an effect that a one-dimensional time-series data compression program recording medium in which a program capable of grasping the error after decompression in advance is recorded.

According to the one-dimensional time-series data compression program recording medium according to claim 37 of the present invention, in the one-dimensional time-series data compression program recording medium according to any one of claims 28 to 31, The calculation of the optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j ≦ m.
If the relation of I (j-1) <I (j) -1 holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) -1 Is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j−
1) If the relationship of ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+) and I (j) + 1 ≧
If the relationship of I (j + 1) holds, the ΔE (1+) is set to 0.If the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is replaced by the node candidate I (j). Exchange to the node candidate I (j) +1, if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, do not exchange the node candidate I (j),
The relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds,
And if ΔE (1-) is equal to or smaller than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is greater than ΔE (1+), the node candidate I
The operation of exchanging (j) for the node candidate I (j) +1 is from j = m-1 to 1
If the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the above operation is performed from j = m-1 to 1. Repeatedly in order, if the exchange of node candidates has not been performed at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold, the process is terminated. Since I recorded the program to be run,
The process of finding the sub-optimal node of the interpolation function can be realized, the compression can be performed according to the properties of the given one-dimensional time series data, and the compression ratio can be controlled by the approximation accuracy, so that the error after decompression can be grasped in advance. There is an effect that a one-dimensional time-series data compression program recording medium on which a program that can be recorded is recorded can be obtained.

According to the one-dimensional time-series data compression program recording medium according to claim 38 of the present invention, in the one-dimensional time-series data compression program recording medium according to any one of claims 28 to 31, there is provided the one-dimensional time-series data compression program recording medium according to claim 28. The calculation of the optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j ≦ m.
If the relation I (j-1) <I (j) -1 holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) -1 Is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j−
1) If the relationship of ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+) and I (j) + 1 ≧
If the relationship of I (j + 1) holds, the ΔE (1+) is set to 0, and if the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of this exchange and the value of the original first objective function are exchanged.
(1-) ≧ 0 and the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and The value of one objective function and the value of the original first objective function are exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) Is not exchanged, the ΔE (1-) <0 and the ΔE (1-) <0
(1 +) <0 holds, and the ΔE (1-) is the ΔE
If (1+) or less, the node candidate I (j) is replaced with the node candidate I
(j) -1 and the value of the first objective function at the time of this exchange and the value of the original first objective function are exchanged, and ΔE (1-) <0 and ΔE (1 +) <0, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) +1, and The operation of exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function is an odd number.
j is performed in ascending order from small to large, and even j is performed in ascending order from large to small, and the value of the first objective function when these series of processes are completed is calculated from the value of the original first objective function. If the threshold value is less than or equal to the value, the operation is performed again in the order of small to large for odd j and in the order of large to small for even j, and whether the exchange of node candidates has not been performed at all. If the value of the first objective function is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the program to be executed is recorded by terminating the processing. The processing to find the optimal node can be realized, and compression can be performed according to the properties of the given one-dimensional time-series data. The compression ratio can be controlled by approximation accuracy. Because, previously grasped one-dimensional time series data compression program recording medium recording a program capable of the error after the extension has an effect to be obtained.

According to the one-dimensional time-series data compression program recording medium according to claim 39 of the present invention, in the one-dimensional time-series data compression program recording medium according to any one of claims 28 to 31, The calculation of the optimal node candidate is performed by giving the index of the node candidate index in ascending order as I (j), 0 ≦ j ≦ m, where I (j−1) <I (j If the relationship of) -1 holds, the value of the first objective function when the node candidate I (j) is exchanged for the node candidate I (j) -1 is calculated, and the value of the first objective function is calculated from the value of the first objective function. 1 Calculate a value ΔE (1-) obtained by subtracting the value of the objective function, and calculate I (j-1) ≧
If the relationship of I (j) -1 holds, the ΔE (1-) is set to 0.If the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) Is replaced with a node candidate I (j) +1, and the value of the first objective function is calculated.
A value ΔE (1+) obtained by subtracting the value of the objective function is calculated, and I (j) + 1 ≧ I (j
+1) is established, the above-mentioned ΔE (1+) is set to 0.If the above-mentioned ΔE (1-) <0 and the above-mentioned ΔE (1+) ≧ 0 are established, the node candidate I (j ) Is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange is exchanged with the value of the original first objective function to obtain the ΔE (1
-) ≧ 0 and the relationship ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the first objective function at the time of the replacement is And the original first
The value of the objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I
(j) is not exchanged, the ΔE (1-) <0 and the ΔE (1+)
<0, and the ΔE (1-) is the ΔE (1+)
If below, the node candidate I (j) is replaced by the node candidate I (j) -1.
The value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged, and the Δ
If the relation of E (1-) <0 and the relation of ΔE (1 +) <0 hold, and the relation of ΔE (1-) is larger than the relation of ΔE (1+), the node candidate I (j) is set to the node The operation of exchanging for the candidate I (j) +1 and exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function is from large to small for odd j. And the even j is performed in ascending order from the smallest to the largest, and the value of the first objective function at the time when a series of these processes is completed is changed to the original first value.
If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the objective function, the above operation is performed again in the order of large to small for the odd j and in the order of small to large for the even j, and the exchange of the node candidates is performed. If not, or if the value of the first objective function is greater than the original value of the first objective function minus a threshold value, then by ending the processing, a program for making the determination is recorded. As a result, it is possible to realize a process for finding a sub-optimal node of the interpolation function, perform compression according to the properties of the given one-dimensional time series data, and control the compression ratio with approximation accuracy, so that errors after decompression can be grasped in advance. There is an effect that a one-dimensional time-series data compression program recording medium on which a program that can be performed is recorded is obtained.

According to the one-dimensional time-series data compression program recording medium of claim 40 of the present invention, in the one-dimensional time-series data compression program recording medium of any one of claims 28 to 31, The calculation of the optimal node candidate is performed by indexing the index of the node candidate in ascending order as I (j), 0 ≤ j ≤ m, where I (j-1) <I (j ) -1 holds, the value of the first objective function when the node candidate I (j) is exchanged for the node candidate I (j) -1 is calculated, and the value of the first objective function is calculated from the value of the first objective function. 1 Calculate a value ΔE (1-) obtained by subtracting the value of the objective function, and calculate I (j-1) ≧
If the relationship of I (j) -1 holds, the ΔE (1-) is set to 0.If the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) Is replaced with a node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function And I (j) + 1 ≧ I (j +
If the relationship of 1) is established, the above ΔE (1+) is set to 0,
If the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is exchanged for the node candidate I (j) -1, and at the time of this exchange. The value of the first objective function is exchanged with the value of the original first objective function, and ΔE (1-) ≧
0 and the relationship ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the value of the first objective function at the time of the replacement is By exchanging the value of the original first objective function, ΔE (1-) ≧ 0 and ΔE
If the relationship of (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE If (1-) is equal to or less than ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the The value of the original first objective function is exchanged, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is greater than ΔE (1+), the node candidate I
(j) is replaced with the node candidate I (j) +1, and the operation of exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange is j = 1. To [m / 2], and from j = m-1 to [m / 2] +1, and the value of the first objective function at the end of these series of processes is the first first function.
If the value is equal to or less than the value of the objective function minus the threshold, the above operation is performed from j = 1 to [m / 2] and j = m−1 to [m / 2].
+1 in order until the node candidates have not been exchanged at all, or if the value of the first objective function is
If it is greater than the value of the objective function minus the threshold,
By ending the processing, a program for making a determination is recorded, so that processing for obtaining a sub-optimal node of the interpolation function can be realized, and compression can be performed according to the properties of given one-dimensional time-series data. Since the ratio can be controlled by the approximation accuracy, there is an effect that a one-dimensional time-series data compression program recording medium in which a program capable of grasping the error after expansion in advance is obtained.

According to the one-dimensional time-series data compression program recording medium of claim 41 of the present invention, in the one-dimensional time-series data compression program recording medium of any one of claims 28 to 31, The calculation of the optimal node candidate is performed by indexing the index of the node candidate in ascending order as I (j), 0 ≤ j ≤ m, where I (j-1) <I (j ) -1 holds, the value of the first objective function when the node candidate I (j) is exchanged for the node candidate I (j) -1 is calculated, and the value of the first objective function is calculated from the value of the first objective function. 1 Calculate a value ΔE (1-) obtained by subtracting the value of the objective function, and calculate I (j-1) ≧
If the relationship of I (j) -1 holds, the ΔE (1-) is set to 0.If the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) Is replaced with a node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function And I (j) + 1 ≧ I (j +
If the relationship of 1) is established, the above ΔE (1+) is set to 0,
If the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is exchanged for the node candidate I (j) -1, and at the time of this exchange. The value of the first objective function is exchanged with the value of the original first objective function, and ΔE (1-) ≧
0 and the relationship ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the value of the first objective function at the time of the replacement is By exchanging the value of the original first objective function, ΔE (1-) ≧ 0 and ΔE
If the relationship of (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE If (1-) is equal to or less than ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the The value of the original first objective function is exchanged, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is greater than ΔE (1+), the node candidate I
(j) is replaced with the node candidate I (j) +1, and the operation of exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange is j = [m / 2] to 1, and
j = [m / 2] +1 to m−1 in order, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function If you do
j = [m / 2] to 1 and j = [m / 2] +1 to m-1 again in order, and the exchange of the node candidates was not performed at all, or the value of the first objective function was If the value is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the process to be performed is recorded by terminating the process, so that the process of obtaining a sub-optimal node of the interpolation function can be realized. One-dimensional time-series data compression program recording that records a program that can perform compression according to the properties of given one-dimensional time-series data and can control the compression ratio with approximation accuracy, so that errors after decompression can be grasped in advance. There is an effect that a medium can be obtained.

According to the one-dimensional time-series data compression program recording medium of claim 42 of the present invention, in the one-dimensional time-series data compression program recording medium of any of claims 28 to 31, The calculation of the optimal node candidate is performed by indexing the index of the node candidate in ascending order as I (j), 0 ≤ j ≤ m, where I (j-1) <I (j ) -1 holds, the value of the first objective function when the node candidate I (j) is exchanged for the node candidate I (j) -1 is calculated, and the value of the first objective function is calculated from the value of the first objective function. 1 Calculate a value ΔE (1-) obtained by subtracting the value of the objective function, and calculate I (j-1) ≧
If the relationship of I (j) -1 holds, the ΔE (1-) is set to 0.If the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) Is replaced with a node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function And I (j) + 1 ≧ I (j +
If the relationship of 1) is established, the above ΔE (1+) is set to 0,
If the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is exchanged for the node candidate I (j) -1, and at the time of this exchange. The value of the first objective function is exchanged with the value of the original first objective function, and ΔE (1-) ≧
0 and the relationship ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the value of the first objective function at the time of the replacement is By exchanging the value of the original first objective function, ΔE (1-) ≧ 0 and ΔE
If the relationship of (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE If (1-) is equal to or less than ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the The value of the original first objective function is exchanged, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is greater than ΔE (1+), the node candidate I
(j) is replaced with the node candidate I (j) +1, and the operation of exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange is j = 1. To m−1, and if the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the above operation is performed from j = 1. m-1 again
If the exchange of the node candidates has not been performed at all or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the program to be executed is completed by terminating the processing. Since it is recorded, it is possible to realize a process of obtaining a sub-optimal node of the interpolation function, perform compression in accordance with the properties of given one-dimensional time series data, and control the compression ratio with approximation accuracy. There is an effect that a one-dimensional time-series data compression program recording medium in which a program capable of grasping an error in advance is recorded is obtained.

According to the one-dimensional time-series data compression program recording medium of claim 43 of the present invention, in the one-dimensional time-series data compression program recording medium of any one of claims 28 to 31, The calculation of the optimal node candidate is performed by indexing the index of the node candidate in ascending order as I (j), 0 ≤ j ≤ m, where I (j-1) <I (j ) -1 holds, the value of the first objective function when the node candidate I (j) is exchanged for the node candidate I (j) -1 is calculated, and the value of the first objective function is calculated from the value of the first objective function. 1 Calculate a value ΔE (1-) obtained by subtracting the value of the objective function, and calculate I (j-1) ≧
If the relationship of I (j) -1 holds, the ΔE (1-) is set to 0.If the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) Is replaced with a node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function And I (j) + 1 ≧ I (j +
If the relationship of 1) is established, the above ΔE (1+) is set to 0,
If the relationship of ΔE (1-) <0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is exchanged for the node candidate I (j) -1, and at the time of this exchange. The value of the first objective function is exchanged with the value of the original first objective function, and ΔE (1-) ≧
0 and the relationship ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the value of the first objective function at the time of the replacement is By exchanging the value of the original first objective function, ΔE (1-) ≧ 0 and ΔE
If the relationship of (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and the ΔE If (1-) is equal to or less than ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the The value of the original first objective function is exchanged, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is greater than ΔE (1+), the node candidate I
(j) is replaced with the node candidate I (j) +1, and the operation of exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange is j = m -1 to 1 in order, and if the value of the first objective function at the end of the series of processes is equal to or less than the original value of the first objective function minus the threshold, the operation is performed by j = m− Repeat from 1 to 1 again,
If the exchange of the node candidates has not been performed at all or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the program to be executed is completed by terminating the processing. Since it is recorded, it is possible to realize a process of obtaining a sub-optimal node of the interpolation function, perform compression in accordance with the properties of given one-dimensional time series data, and control the compression ratio with approximation accuracy. There is an effect that a one-dimensional time-series data compression program recording medium in which a program capable of grasping an error in advance is recorded is obtained.

According to the one-dimensional time-series data compression program recording medium according to claim 44 of the present invention, in the one-dimensional time-series data compression program recording medium according to any one of claims 28 to 31, the final If the determined number of node candidates is equal to or less than the number of data that was not a candidate, the number of node candidates is constituted by an identifier indicating the node candidate, the index number of the finally determined node candidate, and the value of the node candidate. Output the compressed data, and if the finally determined number of node candidates is larger than the number of data that did not become the candidate, an identifier that is not a node candidate and the index number of the data that did not become the node candidate Since a program for outputting compressed data composed of the values of the node candidates is recorded, it is suitable for the properties of given one-dimensional time-series data. Performing compression that has, compression ratio because it can control the accuracy of approximation, one-dimensional time series data compression program storage medium storing a program capable recognizes in advance error after elongation is the effect obtained.

According to a one-dimensional time-series data compression program recording medium according to claim 45 of the present invention, the one-dimensional time-series data compression program recording medium according to any one of claims 26 to 31, The medium is for one-dimensional time-series data that is irregularly spaced with respect to time.
The one-dimensional time-series data compression method is applied independently to time and data, and a program for independently compressing each is included, so that even one-dimensional time-series data at irregular intervals in time can be given. One-dimensional time-series data compression program recording medium storing a program that can perform compression according to the properties of the obtained one-dimensional time-series data and control the compression ratio with approximation accuracy, so that errors after decompression can be grasped in advance. The effect is obtained.

According to a one-dimensional time-series data compression program recording medium according to claim 46 of the present invention, the one-dimensional time-series data compression program recording medium according to any one of claims 26 to 31 is provided. The medium includes a program for compressing the multi-dimensional time-series data by repeatedly applying the one-dimensional time-series data compression method to each of a plurality of one-dimensional time-series data constituting the multi-dimensional time-series data. As a result, the multi-dimensional time-series data can be compressed according to the properties of each one-dimensional time-series data constituting the given multi-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy. To obtain a one-dimensional time-series data compression program recording medium in which a program capable of grasping in advance the error after decompression is recorded. A.

According to the one-dimensional time-series data compression program recording medium of claim 47 of the present invention, the one-dimensional time-series data compression program recording medium of any one of claims 26 to 31 is provided. The medium increases the approximation accuracy value in order from the one-dimensional time-series data of the propagation source to the one-dimensional time-series data in which a plurality of errors propagate, and repeatedly applies the one-dimensional time-series data compression method. Since a program for compressing all the one-dimensional time-series data is included, the compression can be performed in accordance with the properties of the given one-dimensional time-series data without increasing the propagation of error, and the compression ratio is reduced. A one-dimensional time-series data compression program that records a program that can be grasped in advance after decompression because it can be controlled by approximation accuracy. There is an effect that the recording medium can be obtained.

According to the one-dimensional time-series data decompression program recording medium of the forty-eighth aspect of the present invention, the one-dimensional time-series data compression program recording medium of any one of the twenty-sixth, twenty-eighth and twenty-ninth aspects of the present invention A medium storing a program for expanding compressed data compressed by a compressed program, comprising: a first step of inputting compressed compressed data and the number of data when the compressed data is expanded; By interpolating the compressed data using the same interpolation function as the interpolation function, the same number of data as the number of data is calculated, and the time is calculated from the initial time and the time interval by the same number as the number of data. Since a one-dimensional time-series data decompression program including a step and a third step of outputting the data and the time calculated in the second step is recorded, As for the length, since continuity using an interpolation function is used, compressed data compressed by a program recorded in the one-dimensional time-series data compression program recording medium according to claim 26 can be expanded, Moreover, there is an effect that a one-dimensional time-series data decompression program recording medium on which a program capable of decompressing an arbitrary number of data is recorded is obtained.

According to the one-dimensional time-series data expansion program recording medium of claim 49 of the present invention, the program is recorded on the one-dimensional time-series data compression program recording medium of any one of claims 27, 30 and 31. A first step of inputting compressed compressed data and the number of data when the compressed data is decompressed, and a first step of inputting the compressed data and the number of data when decompressing the compressed data; If an identifier indicating that all are 0 is given, the same number of 0s as the number of data and a time equal to the number of data are calculated from the initial time and the time interval. If the identifier indicating that the data is all 0 is not given, the compressed data is interpolated using the same interpolation function as that used for compression, To calculate the data of over data the same number as the number fraction,
A second step of calculating a time from the initial time and the time interval by the same number as the number of data, and a third step of outputting the data and the time calculated in the second step;
The one-dimensional time-series data compression program recording medium according to claim 27, wherein the one-dimensional time-series data compression program according to any one of claims 27, 30, and 31, is configured to record the one-dimensional time-series data decompression program because the continuation by the interpolation function is used for the decompression. There is an effect that a one-dimensional time-series data decompression program recording medium in which a program capable of decompressing compressed data compressed by the recorded program and decompressing an arbitrary number of data is recorded can be obtained.

According to the one-dimensional time-series data expansion program recording medium of claim 50 of the present invention, in the one-dimensional time-series data expansion program recording medium of claim 48 or 49, the one-dimensional time-series data expansion program recording medium is recorded on the medium. The program repeatedly applies the one-dimensional time-series data decompression method to each of the plurality of compressed one-dimensional time-series data constituting the compressed multi-dimensional time-series data, thereby obtaining the compressed multi-dimensional time-series data. The program recorded on the one-dimensional time-series data decompression program recording medium according to claim 48 or 49 is applied to the compressed data of the multi-dimensional time-series data because the program for expanding the series data is included. One-dimensional time-series data expansion that records a program that can expand data in each dimension and expand data in an arbitrary number. The effect of the program recording medium is obtained.

According to a one-dimensional time-series data compression apparatus according to claim 51 of the present invention, there is provided an apparatus for compressing one-dimensional time-series data at equal intervals in time, wherein said one-dimensional time-series data and its approximation accuracy are First means for inputting the
Second means for calculating a node candidate of an interpolation function that approximates the dimensional time-series data, third means for optimizing the position of the node candidate, and the interpolation function based on the node candidate whose position has been optimized. Fourth means for determining an error between the one-dimensional time-series data generated by the above and the original one-dimensional time-series data;
Fifth means for changing the number of nodes when it is determined by the fourth means that the error exceeds a value based on the approximation accuracy, and returning to the second means; Since it is determined that the value does not exceed the value based on the approximation accuracy, the sixth unit that outputs the data of the node candidate and the data of the time corresponding thereto as compressed information is provided. Compression can be performed in accordance with the properties of given one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy, so that errors after decompression can be grasped in advance. There is.

According to a one-dimensional time-series data compression apparatus according to claim 52 of the present invention, there is provided an apparatus for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are First means for inputting the
Second means for determining whether or not data within the approximation accuracy is included in the one-dimensional time-series data; and data within the approximation accuracy is included in the one-dimensional time-series data by the second means. A third means for calculating a candidate node for an interpolation function that approximates the one-dimensional time-series data when it is determined that the one-dimensional time-series data is not included; a fourth means for optimizing the position of the candidate node; A fifth means for judging an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data based on the obtained node candidates; and the fifth means makes the error equal to the approximation accuracy. A sixth means for changing the number of nodes when it is determined to exceed the value based on the second means, and returning to the third means; and the one-dimensional time series data containing data within the approximation accuracy by the second means. Place that is judged to be And outputs information indicating that the one-dimensional time-series data is data within the approximation accuracy. If the fifth means determines that the error does not exceed the value based on the approximation accuracy, the node candidate Since the seventh means for outputting the data and the data at the corresponding time as compressed information is provided, the compression can be performed in accordance with the property of the given one-dimensional time-series data, and the compression ratio is reduced. Since the control can be performed by the approximation accuracy, an error after decompression can be grasped in advance, and furthermore, there is an effect of obtaining a one-dimensional time-series data compression device which can omit the processing for data within the approximation accuracy.

Further, according to the one-dimensional time-series data compression apparatus of claim 53 of the present invention, the means for compressing one-dimensional time-series data at equal time intervals comprises: A first means for calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data by adding an index to the one-dimensional time-series data in the order of the time; A second means for always including the start and end data from the time-series data, and randomly determining only a few node candidates of the nodes;
Third means for interpolating the node candidate by an interpolation function using an index number as an independent variable to calculate an error from the original one-dimensional time-series data; and, from the error, a maximum value of the error and an error average. Fourth means for calculating a value of a first objective function defined by weighted addition with an error variance;
Fifth means for repeatedly changing node candidates so as to minimize the value of the objective function and determining a sub-optimal node candidate;
The quasi-optimal node candidates are interpolated by the interpolation function to generate one-dimensional time-series data approximating the original one-dimensional time-series data, and an error between the one-dimensional time-series data and the original one-dimensional time-series data is calculated. Sixth means for calculating, a seventh means for calculating, from the error, a value of a second objective function defined by weighted addition of a maximum value of the error, an error average, and an error variance; and If the value of the function is equal to or greater than a threshold value corresponding to the approximation accuracy, an eighth means for repeating the processing from the second means to the seventh means by adding an increment to the number of nodes as a new number of nodes And if the value of the second objective function is less than the threshold, the initial time and the time interval of the one-dimensional time series data, the index number of the finally determined node candidate, and the value of the node candidate Ninth means for outputting compressed data Since such comprises, performed is tailored to the nature of the one-dimensional time series data given compression, the compression ratio can be controlled by the approximation accuracy can recognizes in advance errors after extension, 1
There is an effect that a dimensional time series data compression device can be obtained.

According to a one-dimensional time-series data compression apparatus according to claim 54 of the present invention, there is provided an apparatus for compressing one-dimensional time-series data at equal time intervals, wherein the one-dimensional time-series data and its approximation accuracy are A first means for calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data by adding an index to the one-dimensional time-series data in the order of the time; From the time-series data, the second means for always including the start and end data, and determining the node candidates of only the several nodes so as to be approximately equally spaced with respect to the index, and Third means for calculating an error from the original one-dimensional time-series data by interpolating with an interpolation function using an index number as an independent variable; A fourth means for calculating the value of the first objective function defined by the weighted addition; and a step of repeatedly changing the node candidates so as to minimize the value of the first objective function, and determining a sub-optimal node candidate. Means for generating the one-dimensional time-series data approximating the original one-dimensional time-series data by interpolating the sub-optimal node candidates using the interpolation function;
Sixth means for calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data, and, based on the error, a sixth means defined by weighted addition of a maximum value of the error, an error average, and an error variance. Seventh means for calculating the value of the second objective function, and if the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy, a value obtained by adding an increment to the number of nodes is set as a new number of nodes. Eighth means for repeating the processing from the second means to the seventh means, and if the value of the second objective function is less than the threshold value, the initial time and time interval of the one-dimensional time-series data; And the ninth means for outputting compressed data composed of the index numbers of the node candidates determined in (1) and the values of the node candidates, so as to match the properties of the given one-dimensional time-series data. Compression can be performed, and the compression ratio depends on the approximation accuracy. Because it controls, it is possible to advance grasp the error after stretching, the effect of one-dimensional time series data compression device can be obtained.

According to a one-dimensional time-series data compression apparatus according to claim 55 of the present invention, there is provided an apparatus for compressing one-dimensional time-series data at equal time intervals, comprising: First means for inputting an index to the one-dimensional time-series data in the order of time and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; It is determined whether or not all the absolute values of the data are less than or equal to the approximation accuracy. If the absolute value is less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output and the process is terminated. A second means for moving to the first means, a third means for always including the data at the beginning and the end from the one-dimensional time-series data, and randomly determining only a few node candidates of the nodes, Indicate node candidates Fourth means for calculating an error from the original one-dimensional time-series data by interpolating using an interpolation function having the index number as an independent variable, and calculating the maximum value of the error, the error average, and the error variance from the error. Fifth means for calculating the value of the first objective function defined by weighted addition, and changing the node candidate repeatedly so that the value of the first objective function is minimized, and determining the sub-optimal node candidate And means for interpolating the suboptimal node candidates using the interpolation function to generate one-dimensional time-series data approximating the original one-dimensional time-series data, Seventh means for calculating an error from data, and eighth means for calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance. , The value of the second objective function is equal to the approximation accuracy. If it is equal to or greater than the corresponding threshold value, a value obtained by adding an increment to the number of nodes is set as a new number of nodes, and ninth means for repeating the processing from the third means to the eighth means, and the second objective function If the value is less than the threshold value, a compressed data composed of the initial time and the time interval of the one-dimensional time-series data, the index number of the finally determined node candidate and the value of the node candidate is output. 10 means, the compression can be performed according to the properties of the given one-dimensional time-series data, and the compression ratio can be controlled by the approximation accuracy, so that the error after decompression can be grasped in advance, In addition, there is an effect that a one-dimensional time-series data compression apparatus that can omit the processing for data within the approximation accuracy can be obtained.

According to a one-dimensional time-series data compression apparatus according to claim 56 of the present invention, there is provided an apparatus for compressing one-dimensional time-series data at equal time intervals, comprising: First means for inputting an index to the one-dimensional time-series data in order of time and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; It is determined whether or not all the absolute values of the data are less than or equal to the approximation accuracy. If the absolute values are less than or equal to the approximation accuracy, an identifier indicating that they are all 0 is output, and the process is terminated. And the second means for shifting, and among the one-dimensional time series data, the node candidates including only the start and end data and including only a few node candidates so as to be approximately equally spaced with respect to the index. Decide A third means, a fourth means for interpolating the node candidate with an interpolation function using an index number as an independent variable, and calculating an error from the original one-dimensional time-series data; Fifth means for calculating a value of a first objective function defined by weighted addition of a maximum value, an error average, and an error variance, and repeatedly changing node candidates so that the value of the first objective function is minimized Sixth means for determining the sub-optimal node candidates and interpolating the sub-optimal node candidates by the interpolation function to generate one-dimensional time series data approximating the original one-dimensional time series data. Seventh means for calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data, and a second object defined by weighted addition of the maximum value of the error, the average of the error and the error variance from the error Eighth means for calculating a function value If the value of the second objective function is equal to or larger than a threshold value corresponding to the approximation accuracy, the number obtained by adding an increment to the number of nodes is set as a new number of nodes, and the processing from the third means to the eighth means is performed Ninth means to repeat, and if the value of the second objective function is less than the threshold,
A tenth means for outputting compressed data composed of an initial time and a time interval of the one-dimensional time-series data, an index number of a finally determined node candidate, and a value of the node candidate. As a result, compression can be performed in accordance with the properties of given one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy, so that errors after decompression can be grasped in advance. There is an effect that a one-dimensional time-series data compression device that can omit the processing can be obtained.

According to the one-dimensional time-series data compressing apparatus of claim 57 of the present invention, claims 52 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ When j ≤ m, I (j-1) <I
If the relationship (j) -1 holds, node candidate I (j) is
Calculating the value of the first objective function when exchanged for I (j) -1,
A value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated. If I (j-1) ≧ I (j) -1, the ΔE (1-) is calculated.
(1-) is set to 0, and when the relationship of I (j) +1 <I (j + 1) holds, the node candidate I (j) is replaced with the node candidate I (j) +1 The value of the first objective function is calculated, a value ΔE (1+) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j) + 1 ≧ I ( j + 1), the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). +1, the node candidate I (j) is not exchanged if the relation of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds,
The relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds,
And if ΔE (1-) is equal to or smaller than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and the ΔE (1 +) <0
If (1-) is greater than ΔE (1+), the node candidate I
The operation of replacing (j) with the node candidate I (j) +1 is performed in the order of small to large for odd j, and for even j.
j is performed from the largest to the smallest, and
If the value of the first objective function at the end of the series of processes is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operations are performed in the order of small to large for odd j. , And even j are performed again in ascending order from largest to smallest, and no exchange of the node candidates is performed, or the value of the first objective function is obtained by subtracting a threshold value from the value of the original first objective function. If it is larger than the one, the processing is terminated to terminate the processing, so that the processing for obtaining the sub-optimal node of the interpolation function can be realized, and the compression can be performed according to the property of the given one-dimensional time series data. Since the ratio can be controlled by the approximation accuracy, there is an effect that a one-dimensional time-series data compression device that can grasp the error after decompression in advance is obtained.

According to the one-dimensional time-series data compression device of the fifty-eighth aspect of the present invention,
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ When j ≤ m, I (j-1) <I
If the relationship (j) -1 holds, node candidate I (j) is
Calculating the value of the first objective function when exchanged for I (j) -1,
A value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated. If the relationship of I (j-1) ≧ I (j) -1 holds, the value ΔE (1-) is obtained. (1-) is set to 0, and I (j) +1 <I (j +
If the relationship of 1) holds, the value of the first objective function when the node candidate I (j) is exchanged for the node candidate I (j) +1 is calculated, and the value of the first objective function is calculated from the value of the first objective function. Calculate a value ΔE (1+) obtained by subtracting the value of the first objective function of above, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, set the above ΔE (1+) to 0. , The ΔE
If (1-) <0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is replaced with the node candidate I (j) -1, and the Δ
If E (1-) ≧ 0 and the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j) +1, and the ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <
0 and the relationship of ΔE (1 +) <0 holds, and
If E (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0, and if ΔE (1-) is larger than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) +1. Are performed in the order of large to small for odd j, and in the order of small to large for even j, and the value of the first objective function at the time when these series of processing is completed is equal to the original first value. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the objective function, the above operation is performed again in the order of large to small for the odd j and in the order of small to large for the even j, and the exchange of the node candidates is performed Either nothing was done or the value of the first objective function was
If it is greater than the value of the objective function minus the threshold,
By ending the processing, the processing is performed, so that the processing for obtaining the sub-optimal node of the interpolation function can be realized, and the compression according to the property of the given one-dimensional time-series data can be performed.
Since the compression ratio can be controlled by the approximation accuracy, there is an effect that a one-dimensional time-series data compression device that can grasp the error after decompression in advance is obtained.

According to the one-dimensional time-series data compressing apparatus of claim 59 of the present invention,
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ When j ≤ m, I (j-1) <I
If the relationship (j) -1 holds, the node candidate I (j) is
(j) The value of the first objective function when exchanged for -1 is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function is calculated. If the relationship (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) was replaced with the node candidate I (j) +1 was calculated, and the value of the original first objective function was subtracted from the value of the first objective function. Value ΔE
(1+) is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0, and the ΔE If the relationship of (1+) ≧ 0 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j)
(j) is replaced with the node candidate I (j) +1, and the ΔE (1-) ≧ 0
And if the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed, the ΔE (1-) <0 and the Δ
If the relationship of E (1 +) <0 holds and the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate.
If I is replaced by I (j) -1, the relationship of ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds, and if the ΔE (1-) is larger than the ΔE (1+) For example, the node candidate I (j) is replaced with the node candidate I (j).
The operation to exchange for +1 is from j = 1 to [m / 2], and j = m-1
To [m / 2] +1, and if the value of the first objective function at the end of the series of processing is equal to or less than the value of the original first objective function minus the threshold, the above operation is performed. To
j = 1 to [m / 2] and j = m-1 to [m / 2] +1 again in order, and whether the node candidates have not been exchanged at all or the value of the first objective function is If the value is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the process is terminated to perform the process. Therefore, the process of obtaining the sub-optimal node of the interpolation function can be realized.
Since compression can be performed in accordance with the properties of the dimensional time-series data and the compression ratio can be controlled with approximation accuracy, there is an effect that a one-dimensional time-series data compression apparatus capable of grasping in advance errors after decompression can be obtained.

According to the one-dimensional time-series data compressing apparatus of claim 60 of the present invention, claims 53 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ When j ≤ m, I (j-1) <I
If the relationship (j) -1 holds, node candidate I (j) is
Calculating the value of the first objective function when exchanged for I (j) -1, calculating a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, If the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original first objective function is subtracted from the value of the first objective function. Value ΔE
(1+) is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0, and the ΔE If the relationship of (1+) ≧ 0 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, and the ΔE (1-) ≧ 0
And if the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed, the ΔE (1-) <0 and the Δ
The relationship of E (1 +) <0 holds, and the ΔE (1-) is the Δ
If E (1+) or less, the node candidate I (j) is replaced with the node candidate I
(j) -1 and if the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and if the ΔE (1-) is larger than the ΔE (1+), The node candidate I (j) is replaced by the node candidate I (j) +1
To j = [m / 2] to 1 and j = [m /
2] In order from +1 to m−1, if the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the above operation is performed. To j =
[M / 2] to 1 and j = [m / 2] +1 to m-1 again in order, and whether the exchange of the node candidates has not been performed at all or the value of the first objective function is the element If the value is larger than the value obtained by subtracting the threshold value from the value of the first objective function, the process is terminated to terminate the process. Therefore, the process of obtaining a sub-optimal node of the interpolation function can be realized. Since compression can be performed in accordance with the characteristics of the sequence data and the compression ratio can be controlled by approximation accuracy, there is an effect that a one-dimensional time-series data compression device capable of grasping in advance errors after decompression can be obtained.

Also, according to the one-dimensional time-series data compression apparatus of claim 61 of the present invention, claims 53 to 56
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ When j ≤ m, I (j-1) <I
If the relationship (j) -1 holds, node candidate I (j) is
Calculating the value of the first objective function when exchanged for I (j) -1, calculating a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, If the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original first objective function is subtracted from the value of the first objective function. Value ΔE
(1+) is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0, and the ΔE If the relationship of (1+) ≧ 0 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, and the ΔE (1-) ≧ 0
And if the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed, the ΔE (1-) <0 and the Δ
The relationship of E (1 +) <0 holds, and the ΔE (1-) is the Δ
If E (1+) or less, the node candidate I (j) is replaced with the node candidate I
(j) -1 and if the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and if the ΔE (1-) is larger than the ΔE (1+), The node candidate I (j) is replaced by the node candidate I (j) +1
Is performed in order from j = 1 to m-1. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, The above operation was repeated again from j = 1 to m−1, and the exchange of the node candidates was not performed at all, or the value of the first objective function was obtained by subtracting a threshold value from the value of the original first objective function. If it is larger than the one, the processing is terminated to terminate the processing, so that the processing for obtaining the sub-optimal node of the interpolation function can be realized, and the compression according to the property of the given one-dimensional time series data can be performed. Since the ratio can be controlled by the approximation accuracy, there is an effect that a one-dimensional time-series data compression device that can grasp the error after decompression in advance is obtained.

According to the one-dimensional time-series data compressing apparatus of claim 62 of the present invention, claims 53 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j. ≤m, I (j-1) <I
If the relationship (j) -1 holds, node candidate I (j) is
Calculating the value of the first objective function when exchanged for I (j) -1, calculating a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function, If the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and if the relationship of I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original first objective function is subtracted from the value of the first objective function. Value ΔE
(1+) is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0, and the ΔE If the relationship of (1+) ≧ 0 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, and the ΔE (1-) ≧ 0
And if the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed, the ΔE (1-) <0 and the Δ
The relationship of E (1 +) <0 holds, and the ΔE (1-) is the Δ
If E (1+) or less, the node candidate I (j) is replaced with the node candidate I
(j) -1 and if the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and if the ΔE (1-) is larger than the ΔE (1+), The node candidate I (j) is replaced by the node candidate I (j) +1
Is performed in order from j = m-1 to 1. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, The above operation was repeated again from j = m-1 to 1, and the exchange of the node candidates was not performed at all, or the value of the first objective function was obtained by subtracting a threshold value from the value of the original first objective function. If it is larger than the one, the processing is terminated to terminate the processing, so that the processing for obtaining the sub-optimal node of the interpolation function can be realized, and the compression according to the property of the given one-dimensional time series data can be performed. Since the ratio can be controlled by the approximation accuracy, there is an effect that a one-dimensional time-series data compression device that can grasp the error after decompression in advance is obtained.

According to the one-dimensional time-series data compressing apparatus of claim 63 of the present invention, claims 53 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate is performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ When j ≤ m, I (j-1) <I
If the relationship (j) -1 holds, the node candidate I (j) is
(j) The value of the first objective function when exchanged for -1 is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function is calculated. If the relationship (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and if the relationship I (j) +1 <I (j + 1) holds, The value of the first objective function when the node candidate I (j) was replaced with the node candidate I (j) +1 was calculated, and the value of the original first objective function was subtracted from the value of the first objective function. Value ΔE
(1+) is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0, and the ΔE If the relationship of (1+) ≧ 0 holds, the node candidate I (j)
Is exchanged for the node candidate I (j) -1 and the value of the first objective function at the time of this exchange is exchanged with the value of the original first objective function, and the ΔE (1-) ≧ 0 And ΔE (1 +) <0
Is satisfied, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first candidate at the time of this exchange is
The value of the objective function and the value of the original first objective function are exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) If no exchange is performed and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds, and if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate
I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of this exchange and the value of the original first objective function are exchanged, and the ΔE (1 -) <0 and ΔE (1 +) <
0 holds, and the ΔE (1-) is the ΔE (1+)
If greater, the node candidate I (j) is replaced with the node candidate I
(j) +1 and the operation of exchanging the value of the first objective function and the value of the original first objective function at the time of this exchange is performed for odd j, from small to large. The order and the even j are performed in ascending order from the largest to the smallest. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, The above operation is performed again in the order of small to large for the odd j, and in the order of large to small for the even j.
If the value of the objective function is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, the process is terminated, thereby performing the process of obtaining the sub-optimal node of the interpolation function. Since the compression can be performed in accordance with the properties of the given one-dimensional time-series data and the compression ratio can be controlled by the approximation accuracy, an effect is obtained that a one-dimensional time-series data compression device capable of grasping the error after decompression in advance. There is.

According to the one-dimensional time-series data compressing apparatus of claim 64 of the present invention, claims 53 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate may be performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j. ≤m, I (j-1) <I (j)
If the relation of -1 holds, the node candidate I (j) is replaced with the node candidate I (j).
Calculate the value of the first objective function when the value is changed to -1, and
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + If the relationship of 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original is calculated from the value of the first objective function. The value ΔE (1
+), And if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0 and the Δ
If the relationship of E (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original The value of the first objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1 +) <0 hold, the node candidate I (j) is replaced with the node candidate I
(j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged.
If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE
(1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I
(j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1-) <0 and ΔE (1 +) <0
Holds, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j).
+1 and the operation of exchanging the value of the first objective function and the value of the original first objective function at the time of the exchange is performed in the order of the odd j from the largest to the smallest, and the even j J is performed in ascending order from the smallest to the largest, and when these series of processes are completed, the first
If the value of the objective function is equal to or less than the value of the original first objective function minus the threshold value, the operation is performed in the order of large to small for odd j, and small to large for even j. Repeatedly in order, if the exchange of node candidates has not been performed at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold, the process is terminated. , So that a process for finding a sub-optimal node of the interpolation function can be realized, compression can be performed according to the properties of given one-dimensional time-series data, and the compression ratio can be controlled by approximation accuracy. There is an effect that a one-dimensional time-series data compression device capable of grasping a later error in advance can be obtained.

According to the one-dimensional time-series data compressing apparatus of claim 65 of the present invention, claims 53 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate may be performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j. ≤m, I (j-1) <I (j)-
If the relation of 1 holds, the node candidate I (j) is replaced with the node candidate I (j).
Calculate the value of the first objective function when the value is changed to -1, and
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + If the relationship of 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original is calculated from the value of the first objective function. The value ΔE (1
+), And if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0 and the Δ
If the relationship of E (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original The value of the first objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1 +) <0 hold, the node candidate I (j) is replaced with the node candidate I
(j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged.
If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE
(1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I
(j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1-) <0 and ΔE (1 +) <0
Holds, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j).
+1 and the operation of exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function from j = 1 to [m / 2], and j = m-1 to [m / 2] +
1 is performed in order, and if the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is performed from j = 1 to [m / 2], and again from j = m-1 to [m / 2] +1.
If the exchange of the node candidates has not been performed at all or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the decision is made by terminating the process. It is like that.

According to the one-dimensional time-series data compressing apparatus of claim 66 of the present invention, claims 53 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate may be performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j. ≤m, I (j-1) <I (j)-
If the relation of 1 holds, the node candidate I (j) is replaced with the node candidate I (j).
Calculate the value of the first objective function when the value is changed to -1, and
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + If the relationship of 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original is calculated from the value of the first objective function. The value ΔE (1
+), And if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0 and the Δ
If the relationship of E (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original The value of the first objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1 +) <0 hold, the node candidate I (j) is replaced with the node candidate I
(j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged.
If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE
(1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I
(j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1-) <0 and ΔE (1 +) <0
Holds, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j).
+1 and an operation of exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function.
j = [m / 2] to 1 and j = [m / 2] +1 to m−1 in order, and the value of the first objective function at the end of the series of processing is the first first function. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the objective function, the above operation is performed from j = [m / 2] to 1.
And j = [m / 2] +1 to m-1 in order, and whether the node candidates have not been exchanged at all or the value of the first objective function is a threshold value from the value of the original first objective function If the value is larger than the value obtained by subtracting, by ending the processing,
Since it is performed, it is possible to realize a process of finding a sub-optimal node of the interpolation function, perform compression in accordance with the properties of given one-dimensional time-series data, and control the compression ratio with approximation accuracy. Is obtained in order to obtain a one-dimensional time-series data compression apparatus capable of grasping in advance.

According to the one-dimensional time-series data compressing apparatus of claim 67 of the present invention, claims 53 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate may be performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j. ≤m, I (j-1) <I (j)-
If the relation of 1 holds, the node candidate I (j) is replaced with the node candidate I (j).
Calculate the value of the first objective function when the value is changed to -1, and
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + If the relationship of 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original is calculated from the value of the first objective function. The value ΔE (1
+), And if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0 and the Δ
If the relationship of E (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original The value of the first objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1 +) <0 hold, the node candidate I (j) is replaced with the node candidate I
(j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged.
If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE
(1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I
(j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1-) <0 and ΔE (1 +) <0
Holds, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j).
In addition, the operation of exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function is performed in order from j = 1 to m−1, and a series of these operations is performed. If the value of the first objective function at the end of the processing is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operation is performed by j = 1
To m-1 in order, and if the exchange of the node candidates has not been performed at all or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, , The processing for obtaining the sub-optimal node of the interpolation function can be realized, the compression can be performed according to the property of the given one-dimensional time series data, and the compression ratio can be controlled by the approximation accuracy. Therefore, there is an effect that a one-dimensional time-series data compression device capable of grasping in advance the error after decompression is obtained.

According to the one-dimensional time-series data compressing apparatus of claim 68 of the present invention, claims 53 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, the calculation of the sub-optimal node candidate may be performed by numbering the index of the node candidate in ascending order of I (j), 0 ≦ j. ≤m, I (j-1) <I (j)-
If the relation of 1 holds, the node candidate I (j) is replaced with the node candidate I (j).
Calculate the value of the first objective function when the value is changed to -1, and
A value ΔE obtained by subtracting the value of the original first objective function from the value of the objective function
(1-) is calculated, and if the relationship of I (j-1) ≧ I (j) -1 holds, the ΔE (1-) is set to 0, and I (j) +1 <I (j + If the relationship of 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated, and the value of the original is calculated from the value of the first objective function. The value ΔE (1
+), And if the relationship of I (j) + 1 ≧ I (j + 1) holds, the ΔE (1+) is set to 0, the ΔE (1-) <0 and the Δ
If the relationship of E (1+) ≧ 0 holds, the node candidate I (j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the original The value of the first objective function is exchanged, and if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1 +) <0 hold, the node candidate I (j) is replaced with the node candidate I
(j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged.
If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE
(1-) <0 and the relationship of ΔE (1 +) <0 holds, and if ΔE (1-) is equal to or less than ΔE (1+), the node candidate I
(j) is exchanged for the node candidate I (j) -1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged to obtain the ΔE (1-) <0 and ΔE (1 +) <0
Holds, and if ΔE (1-) is greater than ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j).
+1, and the operation of exchanging the value of the first objective function at the time of the exchange and the value of the original first objective function is performed in order from j = m-1 to 1. If the value of the first objective function at the time when the processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operation is performed by j = m−
The processing is repeated again from 1 to 1, and if the exchange of the node candidates has not been performed at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is performed. By ending, the processing is performed to obtain a sub-optimal node of the interpolation function, the compression can be performed according to the properties of the given one-dimensional time-series data, and the compression ratio can be controlled by the approximation accuracy. Thus, there is an effect that a one-dimensional time-series data compression device capable of grasping in advance the error after decompression is obtained.

According to the one-dimensional time-series data compressing apparatus of claim 69 of the present invention, claims 53 to 56 are provided.
In the one-dimensional time-series data compression apparatus according to any one of the above, if the finally determined number of node candidates is equal to or less than the number of data that was not a candidate, the identifier indicating the node candidate and the finally determined Compressed data composed of the index number of the node candidate and the value of the node candidate, and if the number of finally determined node candidates is larger than the number of data that did not become the candidate, Since compressed data composed of an identifier that is not a node candidate, an index number of data that has not become a node candidate, and a value of the node candidate is output, it is adapted to the properties of given one-dimensional time-series data. Since compression can be performed and the compression ratio can be controlled with approximation accuracy, a one-dimensional time-series data compression device that can grasp errors after decompression in advance can be obtained. There is.

According to the one-dimensional time-series data compression apparatus of the seventy-ninth aspect of the present invention,
In the one-dimensional time-series data compression apparatus according to any of the above, for one-dimensional time-series data that is unequally spaced with respect to time, the one-dimensional time-series data compression apparatus is independently applied to time and data, Since each is compressed independently, it is possible to compress even one-dimensional time-series data with unequal intervals in time according to the properties of the given one-dimensional time-series data, and the compression ratio depends on the approximation accuracy. Since control can be performed, there is an effect that a one-dimensional time-series data compression device capable of grasping in advance an error after decompression is obtained.

According to the one-dimensional time-series data compression apparatus of the seventeenth aspect of the present invention,
In the one-dimensional time-series data compression device according to any one of the above, by repeatedly applying the one-dimensional time-series data compression device to each of a plurality of one-dimensional time-series data constituting the multi-dimensional time-series data, Since the multidimensional time series data is compressed, the multidimensional time series data can be compressed according to the properties of each one-dimensional time series data constituting the given multidimensional time series data. Since the compression ratio can be controlled by the approximation accuracy, there is an effect that a one-dimensional time-series data compression device that can grasp the error after decompression in advance is obtained.

According to the one-dimensional time-series data compressing apparatus of claim 72 of the present invention, claims 51 to 56 are provided.
In the one-dimensional time-series data compression device according to any one of the above, for the one-dimensional time-series data in which a plurality of errors propagate, the approximation accuracy value is increased in order from the one-dimensional time-series data of the propagation source. By repeatedly applying the one-dimensional time series data compression apparatus, all the one-dimensional time series data are compressed, so that it is possible to adjust the characteristics of the given one-dimensional time series without increasing the error propagation. Since the compression can be performed and the compression ratio can be controlled by the approximation accuracy, there is an effect that a one-dimensional time-series data compression device that can grasp the error after decompression in advance is obtained.

According to the one-dimensional time-series data decompressing apparatus according to claim 73 of the present invention, the compressed data compressed by the one-dimensional time-series data compressing apparatus according to any one of claims 51, 53 and 54 is provided. A first means for inputting compressed compressed data and the number of data when the compressed data is decompressed, and compressing the compressed data using the same interpolation function as that used for compression. A second means for calculating the same number of data as the number of data by interpolation, and calculating a time from the initial time and the time interval by the same number as the number of data; and the data calculated by the second means. And the third means for outputting the time.
Regarding decompression, since continuity using an interpolation function is used,
A one-dimensional time-series data decompressing apparatus capable of decompressing compressed data compressed by the one-dimensional time-series data compressing apparatus according to any one of claims 51, 53, and 54, and capable of decompressing an arbitrary number of data. There is an effect that can be obtained.

According to the one-dimensional time-series data decompressing apparatus of claim 74 of the present invention, the compressed data compressed by the one-dimensional time-series data compressing apparatus of any one of claims 52, 55 and 56 is provided. A first means for inputting compressed compressed data and the number of data when decompressing the compressed data;
If an identifier indicating that the number of data is equal to the number of data, the time is calculated from the initial time and the time interval by the same number of 0s as the number of data, and the same number of times as the number of data is calculated. When the identifier indicating 0 is not given, the same number of data as the data number is calculated by interpolating the compressed data using the same interpolation function as the interpolation function used at the time of compression. A second means for calculating a time from the initial time and the time interval by the same number as the number of data, and a third means for outputting the data and the time calculated by the second means. Since the continuity using the interpolation function is used for decompression, the compressed data compressed by the one-dimensional time-series data compression device according to claim 52, 55 or 56 can be decompressed.
In addition, there is an effect that a one-dimensional time-series data decompression device capable of decompressing an arbitrary number of data is obtained.

Further, according to the one-dimensional time-series data decompression device according to claim 75 of the present invention, claim 73 or 7
4. The one-dimensional time-series data decompression device according to item 4, wherein a plurality of compressed one-dimensional data constituting the compressed multi-dimensional time-series data
By repeatedly applying the one-dimensional time-series data decompression device to each of the one-dimensional time-series data, the compressed multi-dimensional time-series data is expanded, so that the multi-dimensional time-series data can be compressed. On the other hand, a one-dimensional time-series data decompression device which can decompress data of each dimension by applying the one-dimensional time-series data decompression device according to claim 73 or 74 and can decompress data of an arbitrary number is provided. There is an effect that can be obtained.

[Brief description of the drawings]

FIG. 1 is a processing configuration diagram of a one-dimensional time-series data compression method according to a first embodiment of the present invention.

FIG. 2 is a processing configuration diagram of a one-dimensional time-series data compression method according to the first embodiment of the present invention.

FIG. 3 is a diagram showing a computer used for executing a one-dimensional time-series data compression method and a one-dimensional time-series data expansion method in each embodiment of the present invention.

FIG. 4 is a configuration diagram of a one-dimensional time-series data compression device according to a second embodiment of the present invention.

FIG. 5 is a configuration diagram of a one-dimensional time-series data compression device according to a second embodiment of the present invention.

FIG. 6 is a processing configuration diagram of a one-dimensional time-series data compression method according to a third embodiment of the present invention.

FIG. 7 is a processing configuration diagram of a one-dimensional time-series data compression method according to a third embodiment of the present invention.

FIG. 8 is a configuration diagram of a one-dimensional time-series data compression device according to a fourth embodiment of the present invention.

FIG. 9 is a configuration diagram of a one-dimensional time-series data compression device according to a fourth embodiment of the present invention.

FIG. 10 is an explanatory diagram of a first method of determining a sub-optimal node candidate.

FIG. 11 is an explanatory diagram of a second method of determining a sub-optimal node candidate.

FIG. 12 is an explanatory diagram of one-dimensional time-series data.

FIG. 13 is an explanatory diagram of a node candidate of one-dimensional time-series data.

FIG. 14 is an explanatory diagram of interpolation of node candidates of one-dimensional time-series data.

FIG. 15 is an explanatory diagram of a method of selecting a sub-optimal node candidate.

FIG. 16 is an explanatory diagram of a compressed data format.

FIG. 17 is a processing configuration diagram of a one-dimensional time-series data decompression method according to a fifth embodiment of the present invention.

FIG. 18 is a processing configuration diagram of a one-dimensional time-series data expansion method according to a fifth embodiment of the present invention.

FIG. 19 is a configuration diagram of a one-dimensional time-series data decompression device according to a sixth embodiment of the present invention.

FIG. 20 is a configuration diagram of a one-dimensional time-series data decompression device according to a sixth embodiment of the present invention.

FIG. 21 is a processing configuration diagram of a one-dimensional time-series data decompression method according to a seventh embodiment of the present invention.

FIG. 22 is a processing configuration diagram of a one-dimensional time-series data decompression method according to a seventh embodiment of the present invention.

FIG. 23 is a configuration diagram of a one-dimensional time-series data decompression device according to an eighth embodiment of the present invention.

FIG. 24 is a configuration diagram of a one-dimensional time-series data decompression device according to an eighth embodiment of the present invention.

FIG. 25 is a processing configuration diagram of a multidimensional time-series data compression method according to the ninth embodiment of the present invention.

FIG. 26 is a configuration diagram of a multidimensional time-series data compression device according to a tenth embodiment of the present invention.

FIG. 27 is a processing configuration diagram of a multidimensional time-series data compression method according to the eleventh embodiment of the present invention.

FIG. 28 is a configuration diagram of a multidimensional time-series data compression method according to the twelfth embodiment of the present invention.

[Explanation of symbols]

P1a, P1b, P1c, P1d, P1e, P1f, P
4a, P5a, P4b, P5b, P1, P2, P3, P
4, P5, P6, P7, P8, P9, P10, P11,
P12, P13, P14, P21, P22, P23, P
24, P25, P26, P27, P28, P29, P3
0, P31, P32, P33, P34, P35, P4
1, P42, P43, P44, P45, P46, P4
7, P48, P49, P50, P51, P52, P5
3, P54, P55, P56, P57, P58, P5
9, P61, P62, P63, P64, P65, P6
6, P67, P68, P69, P70, P71, P7
2, P73, P74, P75, P76, P77, P7
8, P79, P101, P101a, P102, P10
3, P104, P105, P106, P107, P10
8, P200, P201, P202, P203, P20
4 Processing, S1, S2, S3, S4, S5, S6, S7, S8, S
9, S11, S12, S13, S14, S15, S1
6, S17, S18, S19, S20 Step 1 CPU 2 Data memory 3 Main memory 4 Input / output device 5 Bus 6 External storage device 40a, 50a Input means 10a Node candidate calculation means 10b Node position optimization means 10c Judgment means 10d Number of nodes Optimizing means 10e determining means 10f determining means 20a data decompressing means 20b data format discriminating means 20c 0 data decompressing means 21 data interpolating means 22 data calculating means 23 time calculating means 24 data format discriminating means 250 0 data calculating means 26 time calculating means 40b Output means 11 index adding means 12 initial node number calculating means 13 node candidate determining means 14 interpolation means 15 error calculating means 16 first objective function calculating means 17 suboptimal node candidate determining means 18 interpolation executing means 19 error calculating means 20 Second eye Function calculating means 21 threshold value determining means 22 number of nodes changing means 23 determination means within approximation accuracy

 ──────────────────────────────────────────────────の Continuation of the front page (54) [Title of Invention] One-dimensional time-series data compression method, one-dimensional time-series data expansion method, one-dimensional time-series data compression program recording medium, one-dimensional time-series data expansion program recording Medium, one-dimensional time-series data compression device, and one-dimensional time-series data decompression device

Claims (75)

[Claims] 1. A method for compressing one-dimensional time-series data at equal time intervals, comprising: a first step of inputting the one-dimensional time-series data and its approximation accuracy; and approximating the one-dimensional time-series data. A second step of calculating a node candidate of an interpolation function; a third step of optimizing the position of the node candidate; and a one-dimensional time series generated by the interpolation function based on the node candidate whose position is optimized. A fourth step of determining an error between the data and the original one-dimensional time-series data; and changing the number of nodes when it is determined in the fourth step that the error exceeds a value based on the approximation accuracy; A fifth step of returning to the second step; and if the error is determined not to exceed a value based on the approximation accuracy in the fifth step, data of the node candidate and data of a time corresponding thereto. And as compressed information Outputting a one-dimensional time-series data compression method. 2. A method for compressing one-dimensional time-series data at equal time intervals, comprising: a first step of inputting the one-dimensional time-series data and its approximation accuracy; A second step of determining whether or not data within the accuracy is included; and a case where it is determined in the second step that the one-dimensional time-series data does not include data within the approximation accuracy. A third step of calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data; a fourth step of optimizing the position of the node candidate; and A fifth step of determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data; and the fifth step determines that the error exceeds a value based on the approximation accuracy. The number of nodes A sixth step of changing and returning to the third step; and determining that the one-dimensional time-series data includes data within the approximation accuracy by the second step. Outputting information indicating that the series data is data within the approximation accuracy, and when the fifth step determines that the error does not exceed the value based on the approximation accuracy, the data of the node candidate and the corresponding And outputting the data of the time to be performed as compressed information. 3. A method for compressing one-dimensional time-series data at equal time intervals, comprising inputting the one-dimensional time-series data and its approximation accuracy, and indexing the one-dimensional time-series data in the order of time. A first step of calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data, and always including start and end data among the one-dimensional time-series data, and randomly A second step of determining only a few node candidates; and a third step of interpolating the node candidates with an interpolation function using an index number as an independent variable to calculate an error from the original one-dimensional time-series data. And a fourth step of calculating, from the error, a value of a first objective function defined by weighted addition of a maximum value of the error, an error average, and an error variance; and To be minimal A fifth step of repeatedly changing the point candidates to determine a sub-optimal node candidate; and interpolating the sub-optimal node candidate by the interpolation function to obtain one-dimensional time series data approximating the original one-dimensional time series data. A sixth step of generating and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; and defining, from the error, a weighted addition of a maximum value of the error, an error average, and an error variance. A seventh step of calculating the calculated value of the second objective function; and, if the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy, adding the increment to the number of nodes to the new number of nodes And an eighth step of repeating the processing from the second step to the seventh step; and if the value of the second objective function is less than the threshold, the initial time and the time interval of the one-dimensional time-series data , The final determined node candidate One-dimensional time series data compression method, which comprises a ninth step of outputting the compressed data constituted by box number and the value of the node candidates. 4. A method for compressing one-dimensional time-series data at equal time intervals, comprising inputting the one-dimensional time-series data and its approximation accuracy, and indexing the one-dimensional time-series data in the order of time. A first step of calculating an initial number of nodes of an interpolation function for adding and interpolating the one-dimensional time-series data; and always including start and end data from the one-dimensional time-series data; A second step of determining node candidates of only a few nodes so as to be approximately equally spaced with respect to, and interpolating the node candidates by an interpolation function using an index number as an independent variable to obtain an original one-dimensional A third step of calculating an error from the series data; and a fourth step of calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance. When A fifth step of repeatedly changing node candidates so as to minimize the value of the first objective function, and determining a sub-optimal node candidate; and interpolating the sub-optimal node candidate by the interpolation function, A sixth step of generating one-dimensional time-series data that approximates the one-dimensional time-series data, and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; A seventh step of calculating the value of the second objective function defined by weighted addition of the maximum value, the error average, and the error variance; and if the value of the second objective function is equal to or greater than a threshold corresponding to the approximation accuracy, An eighth step of repeating the processing from the second step to the seventh step by adding an increment to the number of nodes as a new number of nodes; and if the value of the second objective function is less than the threshold value, , Initial time and time of the one-dimensional time-series data Septum and, finally determined ninth step and one-dimensional time series data compression method, which comprises an outputting compressed data constituted by the index number of the node candidates and the value of the node candidates. 5. A method for compressing one-dimensional time-series data at equal time intervals, comprising inputting the one-dimensional time-series data and its approximation accuracy, and adding an index to the one-dimensional time-series data in order of time. A first step of calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data, and determining whether or not all absolute values of the one-dimensional time-series data are less than or equal to the approximation accuracy, If it is less than or equal to the approximation accuracy, an identifier indicating that it is all 0 is output and the process is terminated. If not, a second process is performed to proceed to a third process described later. A third step of always including the start and end data, and randomly determining only a few node candidates, and interpolating the node candidates by an interpolation function using an index number as an independent variable, One-dimensional time system A fourth step of calculating an error from the data; and a fifth step of calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance. A sixth step of repeatedly changing node candidates so as to minimize the value of the first objective function and determining a sub-optimal node candidate; and interpolating the sub-optimal node candidate by the interpolation function, A seventh step of generating one-dimensional time-series data that approximates the one-dimensional time-series data, and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; An eighth step of calculating the value of the second objective function defined by weighted addition of the maximum value, the error average, and the error variance; and if the value of the second objective function is equal to or greater than a threshold corresponding to the approximation accuracy, Add the number of nodes to the new node A ninth step of repeating the processing from the third step to the eighth step, and if the value of the second objective function is less than the threshold, the initial time and the time interval of the one-dimensional time-series data And a tenth step of outputting compressed data composed of the finally determined index number of the node candidate and the value of the node candidate. 6. A method for compressing one-dimensional time-series data at equal time intervals, comprising inputting the one-dimensional time-series data and its approximation accuracy, and adding an index to the one-dimensional time-series data in order of time. A first step of calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; and determining whether or not all absolute values of the one-dimensional time-series data are less than or equal to the approximation accuracy. 0 if precision is less
A second step of outputting an identifier indicating that the processing is completed, and if not, a second step in which the processing shifts to a third step described later. A third step of determining the node candidates of only several nodes so as to be approximately equidistant with respect to the index, and interpolating the node candidates by an interpolation function using an index number as an independent variable, A fourth step of calculating an error from the original one-dimensional time-series data; and calculating a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance from the error. A fifth step of repeatedly changing node candidates so that the value of the first objective function is minimized, and determining a sub-optimal node candidate; and By interpolation A seventh step of generating one-dimensional time-series data approximating the original one-dimensional time-series data and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; An eighth step of calculating the value of the second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance; and if the value of the second objective function is equal to or greater than a threshold corresponding to the approximation accuracy, For example, a ninth step of repeating the processes from the third step to the eighth step by adding an increment to the number of nodes as a new number of nodes, and a value of the second objective function being less than the threshold value Then, a tenth step of outputting compressed data composed of the initial time and the time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate One-dimensional time-series data characterized by including Compression method. 7. The method according to claim 3, wherein
In the three-dimensional time-series data compression method, the calculation of the sub-optimal node candidate is performed when the index of the node candidate is numbered in ascending order as I (j), 0 ≦ j ≦ m. , I (j-1) <I (j) -1 if node relation I (j)
Is replaced with a node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function If I (j-1) ≧ I (j) -1, set ΔE (1-) to 0, and if the relationship of I (j) +1 <I (j + 1) holds, Node candidate I
calculating the value of the first objective function when (j) is replaced with the node candidate I (j) +1, and calculating the original first value from the value of the first objective function.
Calculate a value ΔE (1+) obtained by subtracting the value of the objective function, and obtain I (j) + 1 ≧ I
If (j + 1), the ΔE (1+) is set to 0, and if the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is set. The node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j ) +1, if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE (1-) < 0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 is from small to large for odd j. The order of the objects and the even j are performed in ascending order from the largest to the smallest, and the value of the first objective function when these series of processes are completed is equal to or less than the value obtained by subtracting the threshold from the value of the original first objective function. Then, the above operation is performed again in the order of small to large for odd j, and in the order of large to small for even j, and whether the node candidates have not been exchanged at all or the first objective function Is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, the processing is terminated to perform the one-dimensional time-series data compression method. 8. The method according to claim 3, wherein
In the three-dimensional time-series data compression method, the calculation of the sub-optimal node candidate is performed when the index of the node candidate is numbered in ascending order as I (j), 0 ≦ j ≦ m. , I (j-1) <I (j) -1 if node relation I (j)
Is replaced with a node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is established. If the above holds, the node candidate
The value of the first objective function when I (j) is replaced with the node candidate I (j) +1 is calculated, and the first first objective function is calculated from the value of the first objective function.
Calculate a value ΔE (1+) obtained by subtracting the value of the objective function, and obtain I (j) + 1 ≧ I
If the relationship (j + 1) holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and the ΔE (1 +) <0 holds, the node candidate I (j) is replaced by the node If the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the ΔE ( 1-) <0 and the relationship of ΔE (1 +) <0 holds,
And, if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the The relation of ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+), the operation of exchanging the node candidate I (j) with the node candidate I (j) +1 is larger for odd j. From the smallest to the largest, and for even j, the smallest to the largest j, the value of the first objective function at the end of the series of processes is obtained by subtracting the threshold value from the value of the original first objective function. If it is less than the above, the above operation is performed again in the order of large to small for odd j and in the order of small to large for even j. If the value of the objective function is larger than the value of the original first objective function minus the threshold, the process is terminated to perform the one-dimensional time-series data compression method. 9. The method according to claim 3, wherein
In the three-dimensional time-series data compression method, the calculation of the sub-optimal node candidate is performed when the index of the node candidate is numbered in ascending order as I (j), 0 ≦ j ≦ m. If the relationship of I (j-1) <I (j) -1 holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) -1 is calculated, A value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated, and I (j-1) ≧ I (j) -1
If the relationship holds, ΔE (1-) is set to 0. If the relationship I (j) +1 <I (j + 1) holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And, if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the The relation of ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+),
The operations of exchanging the node candidate I (j) for the node candidate I (j) +1 are from j = 1 to [m / 2] and j = m-1 to [m / 2] +1.
If the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is performed from j = 1 to [m / 2] and j = m-
1 to [m / 2] +1 in order, and the node candidates are not exchanged at all, or the value of the first objective function is determined by subtracting a threshold value from the value of the original first objective function. If it is larger, the one-dimensional time-series data compression method is performed by terminating the processing. 10. The one-dimensional time-series data compression method according to claim 3, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the relationship ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), an operation of replacing the node candidate I (j) with the node candidate I (j) +1
j = [m / 2] to 1 and j = [m / 2] +1 to m−1 in order, and the value of the first objective function at the time when these series of processes are completed is the first original function. If the value of the objective function is equal to or less than the value obtained by subtracting the threshold, the operation is performed from j = [m / 2] to 1 and j =
[M / 2] +1 to m-1 in order, and the exchange of the node candidates was not performed at all, or the value of the first objective function was obtained by subtracting a threshold value from the value of the original first objective function. A one-dimensional time-series data compression method characterized by performing the processing by terminating the processing if it is larger than the one. 11. The one-dimensional time-series data compression method according to claim 3, wherein the sub-optimal node candidate calculation is performed by numbering indices of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m. If the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the relationship ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), an operation of replacing the node candidate I (j) with the node candidate I (j) +1
j = 1 to m-1 in order, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the above operation is performed. = 1 to m−1 again, and if the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value , One-dimensional time-series data compression method performed by terminating the processing. 12. The method according to claim 3, wherein
In the three-dimensional time-series data compression method, the calculation of the sub-optimal node candidate is performed when the index of the node candidate is numbered in ascending order as I (j), 0 ≦ j ≦ m. , I (j-1) <I (j) -1 if node relation I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the relationship ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), an operation of replacing the node candidate I (j) with the node candidate I (j) +1
j = m-1 to 1 in order, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operation is performed by j = m-1 to 1 in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is greater than the value of the original first objective function minus a threshold value , One-dimensional time-series data compression method performed by terminating the processing. 13. The one-dimensional time-series data compression method according to claim 3, wherein the sub-optimal node candidate calculation is performed by numbering indices of the node candidates in ascending order. Are expressed as I (j), 0 ≤ j ≤ m, and if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j). −1, the value of the first objective function is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function is calculated. 1) ≧ I (j) -1
If the relationship holds, ΔE (1-) is set to 0. If the relationship I (j) +1 <I (j + 1) holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function and the value of the original first objective function at the time of performing the exchange, the ΔE (1-) ≧ 0 and the If the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of this exchange and the element If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1 and the first objective function when the exchange is performed. Is exchanged with the value of the original first objective function, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first when this exchange is performed. The operation of exchanging the value of the objective function and the value of the original first objective function is performed in the order of small to large for odd j, and for even j
Are performed in the order from the largest to the smallest. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold from the value of the original first objective function, the operation is performed in an odd number. j is performed again in ascending order from small to large, and for even j, in ascending order from large to small. Whether the node candidates have not been exchanged at all, or the value of the first objective function is equal to the original first value A method for compressing one-dimensional time-series data, characterized in that the processing is terminated when the value is larger than the value obtained by subtracting the threshold value from the value of the objective function. 14. The one-dimensional time-series data compression method according to claim 3, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. If the relationship is expressed as I (j), 0 ≤ j ≤ m, and if the relationship of I (j-1) <I (j) -1 holds, the node candidate I
The value of the first objective function when (j) is replaced with the node candidate I (j) -1 is calculated, and a value ΔE (1) obtained by subtracting the original value of the first objective function from the value of the first objective function is obtained. -), And if the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and I (j) +1
If the relationship <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated. A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the above ΔE (1+) is calculated. 0, the node candidate I (j) is exchanged for the node candidate I (j) -1 if the relationship of ΔE (1-) <0 and ΔE (1+) ≧ 0 holds. The value of the first objective function at the time of this exchange and the value of the original first objective function are exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, The node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged. 1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged. ΔE (1 -) <0 and the ΔE (1 +) <0 in relation holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
If the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is performed in the order of large to small for the odd j and in the order of small to large for the even j. If the value of the first objective function at the end of is less than or equal to the value of the original first objective function minus the threshold value, the operation is performed in the order of odd j, from large to small, and even j. Is performed again in ascending order from the smallest to the largest. If the node candidates are not exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value , By ending the process One-dimensional time series data compression method and performing decision. 15. The one-dimensional time-series data compression method according to claim 3, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. If the relation is expressed as I (j), 0 ≤ j ≤ m, then if the relation I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
If the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is from j = 1 to [m / 2
] And j = m-1 to [m / 2] +1, and the value of the first objective function when these series of processes are completed is obtained by subtracting the threshold value from the value of the original first objective function. If not, the above operation is repeated again from j = 1 to [m / 2] and from j = m-1 to [m / 2] +1, and whether the exchange of the node candidates has not been performed at all. If the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is terminated to make a decision. Method. 16. The one-dimensional time-series data compression method according to claim 3, wherein the sub-optimal node candidate calculation is performed by numbering indices of the node candidates in ascending order. When the relation is expressed as I (j), 0 ≤ j ≤ m, if the relation of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) +1, and the first objective function at the time of the replacement is replaced. And the original first
The operation of exchanging the value of the objective function is performed in order from j = [m / 2] to 1 and from j = [m / 2] +1 to m−1. If the value of the objective function is equal to or less than the value of the original first objective function minus the threshold, the operation is performed from j = [m / 2] to 1 and j = [m / 2
+1 to m−1 in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value For example, a one-dimensional time-series data compression method, which is performed by terminating processing. 17. The one-dimensional time-series data compression method according to claim 3, wherein the sub-optimal node candidate calculation is performed by numbering the node candidate indexes in ascending order. When the relation is expressed as I (j), 0 ≤ j ≤ m, if the relation of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is performed in order from j = 1 to m-1. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the first objective function, the above operation is repeated again from j = 1 to m-1. If is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, the processing is terminated to perform the one-dimensional time-series data compression method. 18. The one-dimensional time-series data compression method according to claim 3, wherein the sub-optimal node candidate calculation is performed by numbering the node candidate index in ascending order. When the relation is expressed as I (j), 0 ≤ j ≤ m, if the relation of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is performed in order from j = m-1 to 1, and the value of the first objective function at the time when these series of processing is completed is changed to the original value. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the first objective function, the above operation is repeated again from j = m-1 to 1, and the exchange of the node candidates is not performed at all, or the value of the first objective function is determined. Is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, by terminating the process,
Performing a one-dimensional time-series data compression method. 19. The one-dimensional time-series data compression method according to claim 3, wherein when the finally determined number of node candidates is equal to or less than the number of non-candidate data, the node Compressed data composed of an identifier indicating a candidate, the index number of the finally determined node candidate, and the value of the node candidate is output, and if the finally determined number of node candidates is the candidate, If the number of the missing nodes is larger than the number of missing nodes, compressed data composed of an identifier that is not a node candidate, an index number of the data that did not become the node candidate, and the value of the node candidate is output. Series data compression method. 20. The one-dimensional time-series data compression method according to claim 1, wherein the one-dimensional time-series data compression method is applied to one-dimensional time-series data having unequal intervals in time. A one-dimensional time-series data compression method characterized by independently applying time and data and compressing each independently. 21. The one-dimensional time-series data compression method according to claim 1, wherein each of the plurality of one-dimensional time-series data constituting the multi-dimensional time-series data is compared with the one-dimensional time-series data. A one-dimensional time-series data compression method, wherein multi-dimensional time-series data is compressed by repeatedly applying a data compression method. 22. The one-dimensional time-series data compression method according to claim 1, wherein the one-dimensional time-series data in which a plurality of errors propagate is obtained from the one-dimensional time-series data of a propagation source. A one-dimensional time-series data compression method characterized in that all the one-dimensional time-series data is compressed by sequentially increasing the approximation accuracy value and repeatedly applying the one-dimensional time-series data compression method. 23. A method for decompressing compressed data compressed by the one-dimensional time-series data compression method according to claim 1, wherein the compressed data and the compressed data are decompressed. A first step of inputting the number of data, and interpolating the compressed data using the same interpolation function as used in the compression to calculate the same number of data as the number of data. And a second step of calculating a time from the time interval by the same number as the number of data, and a third step of outputting the data and the time calculated in the second step. One-dimensional time series data decompression method. 24. A method for decompressing compressed data compressed by the one-dimensional time-series data compression method according to claim 2, wherein the compressed data and the compressed data are decompressed. A first step of inputting the number of data, and when an identifier indicating that the data is all 0 is added to the compressed data, 0, which is the same as the number of data, an initial time and a time interval Calculate the time by the same number as the number of data, and if the compressed data does not have an identifier indicating that the data is all 0, use the same interpolation function as that used in the compression. Interpolating the compressed data to calculate the same number of data as the number of data, and calculating the time from the initial time and the time interval by the same number as the number of data; and the second step The data calculated in And a third step of outputting the time and the time. 25. The one-dimensional time-series data decompression method according to claim 23, wherein each of the plurality of compressed one-dimensional time-series data constituting the compressed multi-dimensional time-series data is subjected to the one-dimensional time-series data. A one-dimensional time-series data decompression method characterized in that compressed multi-dimensional time-series data is decompressed by repeatedly applying the time-series data decompression method. 26. A medium recording a program for compressing one-dimensional time-series data at equal time intervals, comprising: a first step of inputting the one-dimensional time-series data and its approximation accuracy; A second step of calculating a node candidate of an interpolation function that approximates data; a third step of optimizing the position of the node candidate; and a step in which the position is generated by the interpolation function based on the optimized node candidate. A fourth step of determining an error between the one-dimensional time-series data and the original one-dimensional time-series data; and a node number when the fourth step determines that the error exceeds a value based on the approximation accuracy. And returning to the second step. If the error is determined not to exceed the value based on the approximation accuracy in the fifth step, the data of the node candidate and the corresponding Time data and A one-dimensional time-series data compression program recording medium, comprising: a sixth step of outputting as a compressed information. 27. A medium recording a program for compressing one-dimensional time-series data at equal time intervals, comprising: a first step of inputting the one-dimensional time-series data and its approximation accuracy; A second step of determining whether or not data within the approximation accuracy is included in the data; and determining that the one-dimensional time-series data does not include data within the approximation accuracy by the second step. A third step of calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data in the case where the one-dimensional time-series data is approximated; a fourth step of optimizing a position of the node candidate; and a node whose position is optimized. A fifth step of determining an error between the one-dimensional time-series data generated by the interpolation function based on the candidate and the original one-dimensional time-series data; Over and over A sixth step of changing the number of nodes when the connection is cut off and returning to the third step; and judging that the one-dimensional time-series data includes data within the approximation accuracy by the second step. Output the information that the one-dimensional time-series data is within the approximation accuracy if the error is determined to not exceed the value based on the approximation accuracy in the fifth step. A one-dimensional time-series data compression program characterized by recording a one-dimensional time-series data compression program including a seventh step of outputting node candidate data and time data corresponding thereto as compressed information. recoding media. 28. A medium on which a program for compressing one-dimensional time-series data at equal time intervals is recorded, wherein the one-dimensional time-series data and its approximation accuracy are inputted, and the time of the one-dimensional time-series data is compared with the time. A first step of calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data by adding an index in the order of, and always includes data at the beginning and end of the one-dimensional time-series data. And a second step of randomly determining only a few node candidates, and interpolating the node candidates by an interpolation function using an index number as an independent variable, and calculating an error from the original one-dimensional time-series data. A third step of calculating; a fourth step of calculating, from the error, a value of a first objective function defined by weighted addition of a maximum value of the error, an error average, and an error variance; function A fifth step of repeatedly changing node candidates so as to minimize the value and determining a sub-optimal node candidate; approximating the original one-dimensional time-series data by interpolating the sub-optimal node candidate using the interpolation function A sixth step of generating one-dimensional time-series data to be calculated, and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; A seventh step of calculating a value of a second objective function defined by weighted addition with variance; and if the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy, add an increment to the number of nodes. An eighth step of repeating the processing from the second step to the seventh step using the calculated value as a new number of nodes; and if the value of the second objective function is less than the threshold value, the one-dimensional time-series data Final time and time interval, and finally decided One-dimensional time-series data compression program including a ninth step of outputting compressed data composed of the index numbers of the selected node candidates and the values of the node candidates. Compressed program recording medium. 29. A medium in which a program for compressing one-dimensional time-series data at equal time intervals is recorded, wherein the one-dimensional time-series data and its approximation accuracy are inputted, and the time of the one-dimensional time-series data is compared with the time. A first step of calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data by adding an index in the order of, and always includes data at the beginning and end of the one-dimensional time-series data. And a second step of determining node candidates of only a few nodes so as to be approximately equally spaced with respect to the index; and interpolating the node candidates by an interpolation function using an index number as an independent variable. A third step of calculating an error with the one-dimensional time-series data of the following; and, from the error, a value of a first objective function defined by weighted addition of a maximum value of the error, an error average, and an error variance A fourth step of calculating; a fifth step of repeatedly changing node candidates so as to minimize the value of the first objective function to determine a sub-optimal node candidate; and interpolating the sub-optimal node candidate. A sixth step of generating one-dimensional time-series data approximating the original one-dimensional time-series data by interpolating using the function, and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; A seventh step of calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance; If the value is equal to or more than the threshold value corresponding to the above, an eighth step of repeating the processing from the second step to the seventh step by adding the increment to the number of nodes as a new number of nodes, and the second objective function Is less than the threshold, the one-dimensional time series Ninth step of outputting compressed data composed of the initial time and time interval of the data, the index number of the finally determined node candidate, and the value of the node candidate. A one-dimensional time-series data compression program recording medium characterized by recording a program. 30. A medium in which a program for compressing one-dimensional time-series data at equal intervals of time is recorded, wherein the one-dimensional time-series data and its approximation accuracy are input, and the one-dimensional time-series data is input in the order of time. A first step of adding an index and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data, and determining whether or not all absolute values of the one-dimensional time-series data are below the approximation accuracy A second step of outputting an identifier indicating that the value is all 0 if the accuracy is less than the approximation accuracy, and terminating the processing; otherwise, moving to a third step described later; A third step of randomly determining node candidates of only a few nodes, including data at the beginning and end of data, and interpolating the node candidates by an interpolation function using an index number as an independent variable. A fourth step of calculating an error from the original one-dimensional time-series data; and, from the error, a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance. A fifth step of calculating a value, a sixth step of repeatedly changing node candidates so as to minimize the value of the first objective function, and determining a sub-optimal node candidate, A seventh step of generating one-dimensional time-series data approximating the original one-dimensional time-series data by interpolating using the interpolation function and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data An eighth step of calculating, from the error, a value of a second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance; If it is equal to or greater than the threshold value corresponding to the accuracy, the number of nodes is incremented. A ninth step of repeating the processing from the third step to the eighth step by using the added value as a new number of nodes; and, if the value of the second objective function is less than the threshold value, the one-dimensional time series A one-dimensional time-series data compression program including a tenth step of outputting compressed data composed of an initial time and a time interval of data, an index number of a finally determined node candidate, and a value of the node candidate A one-dimensional time-series data compression program recording medium characterized by recording a program. 31. A medium on which a program for compressing one-dimensional time-series data at equal intervals of time is recorded, wherein the one-dimensional time-series data and its approximation accuracy are input, and the one-dimensional time-series data is input in the order of time. A first step of adding an index and calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; and determining whether or not all absolute values of the one-dimensional time-series data are below the approximation accuracy. Is performed, and if the value is less than the approximation accuracy, all values are 0.
A second step of outputting an identifier indicating that the processing is completed, and if not, a second step in which the processing shifts to a third step described later. A third step of determining the node candidates of only several nodes so as to be approximately equidistant with respect to the index, and interpolating the node candidates by an interpolation function using an index number as an independent variable, A fourth step of calculating an error from the original one-dimensional time-series data; and calculating a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance from the error. A fifth step of repeatedly changing node candidates so that the value of the first objective function is minimized, and determining a sub-optimal node candidate; and By interpolation A seventh step of generating one-dimensional time-series data approximating the original one-dimensional time-series data and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; An eighth step of calculating the value of the second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance; and if the value of the second objective function is equal to or greater than a threshold corresponding to the approximation accuracy, For example, a ninth step of repeating the processing from the third step to the eighth step by adding an increment to the number of nodes to a new number of nodes, and the value of the second objective function being less than the threshold value Then, a tenth step of outputting compressed data composed of the initial time and the time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate is performed. Including a one-dimensional time series data compression program A one-dimensional time-series data compression program recording medium characterized by being recorded. 32. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with a node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function If I (j-1) ≧ I (j) -1, set ΔE (1-) to 0, and if the relationship of I (j) +1 <I (j + 1) holds, Node candidate I
calculating the value of the first objective function when (j) is replaced with the node candidate I (j) +1, and calculating the original first value from the value of the first objective function.
Calculate a value ΔE (1+) obtained by subtracting the value of the objective function, and obtain I (j) + 1 ≧ I
If (j + 1), the ΔE (1+) is set to 0, and if the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is set. The node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j ) +1, if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE (1-) < 0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 is from small to large for odd j. The order of the objects and the even j are performed in ascending order from the largest to the smallest, and the value of the first objective function at the end of the series of processes is equal to or less than the value obtained by subtracting the threshold from the value of the original first objective function. Then, the above operation is performed again in the order of small to large for the odd j, and in the order of large to small for the even j. Is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, the processing is terminated to perform the processing. 33. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order. Is expressed as I (j), 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with a node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is established. If the above holds, the node candidate
The value of the first objective function when I (j) is replaced with the node candidate I (j) +1 is calculated, and the first first objective function is calculated from the value of the first objective function.
Calculate a value ΔE (1+) obtained by subtracting the value of the objective function, and obtain I (j) + 1 ≧ I
If the relationship (j + 1) holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and the ΔE (1 +) <0 holds, the node candidate I (j) is replaced by the node If the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the ΔE ( 1-) <0 and the relationship of ΔE (1 +) <0 holds,
And, if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the The relation of ΔE (1 +) <0 holds,
And, if ΔE (1-) is larger than ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 is larger for odd j. From the smallest to the largest, and for even j, the smallest to the largest j, the value of the first objective function at the end of the series of processes is obtained by subtracting the threshold value from the value of the original first objective function. If not, the above operation is performed again in the order of large to small for the odd j and in the order of small to large for the even j. If the value of the objective function is greater than the value obtained by subtracting the threshold value from the value of the original first objective function, the processing is terminated to execute the processing. . 34. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the sub-optimal node candidate calculation is performed by numbering the node candidate index in ascending order. Is expressed as I (j), 0 ≤ j ≤ m. If the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I ( j) The value of the first objective function when exchanged for -1 is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated. j-1) ≧ I (j) -1
If the relationship holds, ΔE (1-) is set to 0. If the relationship I (j) +1 <I (j + 1) holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And, if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the The relation of ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+),
The operations of exchanging the node candidate I (j) for the node candidate I (j) +1 are from j = 1 to [m / 2] and j = m-1 to [m / 2] +1.
If the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is performed from j = 1 to [m / 2] and j = m-
1 to [m / 2] +1 in order, and the exchange of the node candidates is not performed at all, or the value of the first objective function is determined by subtracting a threshold value from the value of the original first objective function. If it is larger, the one-dimensional time-series data compression program recording medium is to be executed by terminating the processing. 35. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the calculation of the sub-optimal node candidates is performed by numbering the indexes of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the relationship ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), an operation of replacing the node candidate I (j) with the node candidate I (j) +1
j = [m / 2] to 1 and j = [m / 2] +1 to m−1 in order, and the value of the first objective function at the time when these series of processes are completed is the first original function. If the value of the objective function is equal to or less than the value obtained by subtracting the threshold, the operation is performed from j = [m / 2] to 1 and j =
[M / 2] +1 to m-1 in order, and the exchange of the node candidates was not performed at all, or the value of the first objective function was obtained by subtracting a threshold value from the value of the original first objective function. A one-dimensional time-series data compression program recording medium characterized in that the processing is completed by terminating the processing if it is larger than the one. 36. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the calculation of the sub-optimal node candidates is performed by numbering the indexes of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the relationship ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), an operation of replacing the node candidate I (j) with the node candidate I (j) +1
j = 1 to m-1 in order, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the above operation is performed. = 1 to m−1 again, and if the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value A one-dimensional time-series data compression program recording medium, which is executed by terminating processing. 37. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the calculation of the sub-optimal node candidates is performed by numbering the indexes of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m. If the relation of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the relationship ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), an operation of replacing the node candidate I (j) with the node candidate I (j) +1
j = m-1 to 1 in order, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value of the original first objective function minus the threshold, the operation is performed by j = m-1 to 1 in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is greater than the value of the original first objective function minus a threshold value A one-dimensional time-series data compression program recording medium, which is executed by terminating processing. 38. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order. Is expressed as I (j), 0 ≤ j ≤ m. If the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I ( j) The value of the first objective function when exchanged for -1 is calculated, and a value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is calculated. j-1) ≧ I (j) -1
If the relationship holds, ΔE (1-) is set to 0. If the relationship I (j) +1 <I (j + 1) holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function and the value of the original first objective function at the time of performing the exchange, the ΔE (1-) ≧ 0 and the If the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of this exchange and the element If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1 and the first objective function when the exchange is performed. Is exchanged with the value of the original first objective function, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first when this exchange is performed. The operation of exchanging the value of the objective function and the value of the original first objective function is performed in the order of small to large for odd j, and for even j
Is performed in the order from the largest to the smallest. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold value from the value of the original first objective function, the operation is performed in an odd number. j is performed again in ascending order from small to large, and for even j, in ascending order from large to small. Whether the node candidates have not been exchanged at all or the value of the first objective function is equal to the original first value A one-dimensional time-series data compression program recording medium characterized in that the processing is completed by terminating the processing if it is larger than the value obtained by subtracting the threshold value from the value of the objective function. 39. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. When the result is expressed as I (j), 0 ≤ j ≤ m, if the relationship I (j-1) <I (j) -1 holds, the node candidate I
The value of the first objective function when (j) is replaced with the node candidate I (j) -1 is calculated, and a value ΔE (1) obtained by subtracting the original value of the first objective function from the value of the first objective function is obtained. -), And if the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and I (j) +1
If the relationship <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated. A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the above ΔE (1+) is calculated. 0, the node candidate I (j) is exchanged for the node candidate I (j) -1 if the relationship of ΔE (1-) <0 and ΔE (1+) ≧ 0 holds. The value of the first objective function at the time of this exchange and the value of the original first objective function are exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, The node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged. 1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged. ΔE (1 -) <0 and the ΔE (1 +) <0 in relation holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
If the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is performed in the order of large to small for the odd j and in the order of small to large for the even j. If the value of the first objective function at the end of is less than or equal to the value of the original first objective function minus the threshold value, the operation is performed in the order of odd j, from large to small, and even j. Is performed again in ascending order from the smallest to the largest. If the node candidates are not exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value , By ending the process One-dimensional time series data compression program recording medium characterized in that to make a decision. 40. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the sub-optimal node candidate calculation is performed by numbering the node candidate index in ascending order. When the result is expressed as I (j), 0 ≤ j ≤ m, if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
If the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is from j = 1 to [m / 2
] And j = m-1 to [m / 2] +1, and the value of the first objective function at the end of the series of processing is obtained by subtracting the threshold value from the value of the original first objective function. If not, the above operation is repeated again from j = 1 to [m / 2] and from j = m-1 to [m / 2] +1, and whether the exchange of the node candidates has not been performed at all. If the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is terminated to make the determination. Serial data compression program recording medium. 41. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. When the result is expressed as I (j), 0 ≤ j ≤ m, if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) +1, and the first objective function at the time of the replacement is replaced. And the original first
The operation of exchanging the value of the objective function is performed in order from j = [m / 2] to 1 and from j = [m / 2] +1 to m−1. If the value of the objective function is equal to or less than the value of the original first objective function minus the threshold, the operation is performed from j = [m / 2] to 1 and j = [m / 2
+1 to m−1 in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is greater than the value of the original first objective function minus a threshold value For example, a one-dimensional time-series data compression program recording medium, which is performed by terminating processing. 42. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the sub-optimal node candidate calculation is performed by numbering the node candidate index in ascending order. When the result is expressed as I (j), 0 ≤ j ≤ m, if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is An operation of exchanging the value of the function and the value of the original first objective function is performed in order from j = 1 to m−1, and the value of the first objective function when these series of processes are completed is changed to the original value. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the first objective function, the above operation is repeated again from j = 1 to m-1. Is larger than a value obtained by subtracting a threshold value from the original value of the first objective function, the processing is terminated to execute the processing. 43. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidate in ascending order. When the result is expressed as I (j), 0 ≤ j ≤ m, if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is performed in order from j = m-1 to 1, and the value of the first objective function at the time when these series of processing is completed is changed to the original value. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the first objective function, the above operation is repeated again from j = m-1 to 1, and the exchange of the node candidates is not performed at all, or the value of the first objective function is determined. Is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, by terminating the process,
A one-dimensional time-series data compression program recording medium, characterized in that: 44. The one-dimensional time-series data compression program recording medium according to claim 28, wherein the finally determined number of node candidates is equal to or less than the number of non-candidate nodes. Output compressed data composed of an identifier indicating the node candidate, the index number of the finally determined node candidate, and the value of the node candidate, and the number of the finally determined node candidates is the candidate If the number of pieces of data is not larger than the number of pieces of unsatisfied nodes, compressed data composed of an identifier that is not a node candidate, an index number of the data that is not a pieces of the node candidates, and a value of the node candidate is output. Dimensional time series data compression program recording medium. 45. The one-dimensional time-series data compression program recording medium according to claim 26, wherein said recording medium stores the one-dimensional time-series data compressed at irregular intervals with respect to time. A one-dimensional time-series data compression program recording medium, characterized by including a program for independently applying the one-dimensional time-series data compression method for time and data, and for independently compressing each. 46. The one-dimensional time-series data compression program recording medium according to claim 26, wherein the recording medium stores a plurality of one-dimensional time-series data constituting multidimensional time-series data. On the other hand, a one-dimensional time-series data compression program recording medium characterized by including a program for compressing multi-dimensional time-series data by repeatedly applying the one-dimensional time-series data compression method. 47. The one-dimensional time-series data compression program recording medium according to any one of claims 26 to 31, wherein the recording medium is a transmission source for one-dimensional time-series data in which a plurality of errors propagate. And a program that compresses all the one-dimensional time-series data by sequentially increasing the approximation accuracy value from the one-dimensional time-series data and repeatedly applying the one-dimensional time-series data compression method. One-dimensional time-series data compression program recording medium. 48. A medium storing a program for expanding compressed data compressed by a program recorded on the one-dimensional time-series data compression program recording medium according to claim 26, 28 or 29, A first step of inputting the compressed data and the number of data when the data is decompressed; and interpolating the compressed data using the same interpolation function as that used in the compression to obtain the data number. A second step of calculating the same number of data as the first time and calculating the time from the initial time and the time interval by the same number as the number of data; and a second step of outputting the data and the time calculated in the second step. A one-dimensional time-series data decompression program recording medium, which records a one-dimensional time-series data decompression program including the steps of: 49. A medium on which a program for expanding compressed data compressed by a program recorded on the one-dimensional time-series data compression program recording medium according to claim 27, 30 or 31, is recorded. A first step of inputting the compressed data and the number of data when the data is decompressed; and, if the compressed data is provided with an identifier indicating that the data is all 0, the number of data and The time is calculated from the same number of 0s, the initial time and the time interval by the same number as the number of data, and when the compressed data is not provided with an identifier indicating that all the data is 0, the compression time By interpolating the compressed data using the same interpolation function as the interpolation function used, the same number of data as the number of data is calculated, and the time is calculated from the initial time and the time interval as the number of data. A one-dimensional time-series data decompression program including a second step of calculating minutes and a third step of outputting the data and the time calculated in the second step is recorded. Dimensional time series data expansion program recording medium. 50. The one-dimensional time-series data expansion program recording medium according to claim 48 or 49, wherein the program recorded on the medium is a plurality of compressed one-dimensional data constituting compressed multi-dimensional time-series data. A one-dimensional time-series data expansion program characterized by including a program for expanding compressed multi-dimensional time-series data by repeatedly applying the one-dimensional time-series data expansion method to each of the time-series data. recoding media. 51. An apparatus for compressing one-dimensional time-series data at equal time intervals, a first means for inputting the one-dimensional time-series data and its approximation accuracy, and approximating the one-dimensional time-series data. Second means for calculating a node candidate of an interpolation function; third means for optimizing the position of the node candidate; and a one-dimensional time series generated by the interpolation function based on the node candidate whose position is optimized. Fourth means for determining an error between the data and the original one-dimensional time-series data; and changing the number of nodes when the fourth means determines that the error exceeds a value based on the approximation accuracy; Fifth means returning to the second means, and data of the node candidate and data of time corresponding thereto when it is determined by the fifth means that the error does not exceed a value based on the approximation accuracy. And compressed information A one-dimensional time-series data compression apparatus, comprising: 52. An apparatus for compressing one-dimensional time-series data at equal time intervals, comprising: first means for inputting the one-dimensional time-series data and its approximation accuracy; Second means for determining whether or not data within the accuracy is included; and when the second means determines that the data within the approximation accuracy is not included in the one-dimensional time-series data, Third means for calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data; fourth means for optimizing the position of the node candidate; and Fifth means for determining an error between the one-dimensional time-series data generated by the interpolation function and the original one-dimensional time-series data, and the fifth means determines that the error exceeds a value based on the approximation accuracy. If the said A seventh means returning to the third means; and, if it is determined by the second means that the one-dimensional time-series data contains data within the approximation accuracy, the one-dimensional time-series data is converted to the approximation accuracy. Information indicating that the data is within the range, and when the fifth means determines that the error does not exceed the value based on the approximation accuracy, the data of the node candidate and the data of the time corresponding thereto are And a seventh unit for outputting the compressed information as compressed information. 53. An apparatus for compressing one-dimensional time-series data at equal time intervals, comprising inputting the one-dimensional time-series data and its approximation accuracy, and indexing the one-dimensional time-series data in the order of time. First means for calculating an initial number of nodes of an interpolation function for adding and interpolating the one-dimensional time-series data; and always including start and end data among the one-dimensional time-series data and randomly. A second means for determining node candidates of only a few nodes; and a third means for interpolating the node candidates with an interpolation function using an index number as an independent variable to calculate an error from the original one-dimensional time-series data. Means for calculating, from the error, a value of a first objective function defined by weighted addition of a maximum value of the error, an error average, and an error variance; and To be minimal Fifth means for repeatedly changing node candidates to determine sub-optimal node candidates, and interpolating the sub-optimal node candidates by the interpolation function to obtain one-dimensional time series data approximating the original one-dimensional time series data Sixth means for generating and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; and defining from the error a weighted addition of a maximum value of the error, an error average and an error variance. Seventh means for calculating the value of the calculated second objective function, and if the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy, the value obtained by adding an increment to the number of nodes is used as the new number of nodes. Eighth means for repeating the processing from the second means to the seventh means, and if the value of the second objective function is less than the threshold value, the initial time and time interval of the one-dimensional time-series data , The final candidate node Time series data compression apparatus 1 dimensional, characterized in that a ninth means for outputting the compressed data made up of a box number and value of the node candidates. 54. An apparatus for compressing one-dimensional time-series data at equal time intervals, comprising inputting the one-dimensional time-series data and its approximation accuracy, and indexing the one-dimensional time-series data in the order of time. First means for calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; and always including start and end data among the one-dimensional time-series data, and the index Second means for determining node candidates of only a few nodes so as to be approximately equally spaced with respect to, and interpolating the node candidates with an interpolation function using an index number as an independent variable to obtain an original one-dimensional A third means for calculating an error from the series data; and a fourth means for calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance. Fifth means for repeatedly changing node candidates so as to minimize the value of the first objective function, and determining a sub-optimal node candidate; interpolating the sub-optimal node candidate by the interpolation function; Sixth means for generating one-dimensional time-series data approximating the one-dimensional time-series data, and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; A seventh means for calculating a value of a second objective function defined by weighted addition of the maximum value of the error average and the error variance of the second objective function; An eighth means for repeating the processing from the second means to the seventh means by adding a value obtained by adding an increment to the number of nodes to a new number of nodes; and if the value of the second objective function is less than the threshold value, For example, the initial time and time of the one-dimensional time series data Interval and, series data compression apparatus when one-dimensional, characterized in that it comprises a ninth means for outputting the compressed data made up of an index number of the last-determined node candidates and the value of the node candidates. 55. An apparatus for compressing one-dimensional time-series data at equal time intervals, comprising inputting the one-dimensional time-series data and its approximation accuracy, and adding an index to the one-dimensional time-series data in order of time. First means for calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data, and determining whether or not absolute values of the one-dimensional time-series data are all less than or equal to the approximation accuracy, If it is less than or equal to the approximation accuracy, an identifier indicating that it is all 0 is output and the process is terminated. If not, a second unit is shifted to a third unit to be described later. A third means for always including the start and end data, and randomly determining only a few node candidates; and interpolating the node candidates by an interpolation function using an index number as an independent variable, 1D time A fourth means for calculating an error from the column data; and a fifth means for calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance. And sixth means for repeatedly changing node candidates so that the value of the first objective function is minimized to determine a sub-optimal node candidate; and interpolating the sub-optimal node candidate by the interpolation function, Seventh means for generating one-dimensional time-series data approximating the original one-dimensional time-series data and calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data; Eighth means for calculating a value of the second objective function defined by weighted addition of the maximum value of the error average and the error variance of the second objective function, and if the value of the second objective function is equal to or greater than a threshold corresponding to the approximation accuracy , Adding the increment to the number of nodes Ninth means for repeating the processing from the third means to the eighth means as a score, and if the value of the second objective function is less than the threshold value, the initial time and the time interval of the one-dimensional time-series data 10. A one-dimensional time-series data compression apparatus, comprising: tenth means for outputting compressed data composed of an index number of a node candidate finally determined and a value of the node candidate. 56. An apparatus for compressing one-dimensional time-series data at equal time intervals, comprising inputting the one-dimensional time-series data and its approximation accuracy, and adding an index to the one-dimensional time-series data in order of time. First means for calculating an initial number of nodes of an interpolation function for interpolating the one-dimensional time-series data; and determining whether or not all absolute values of the one-dimensional time-series data are less than or equal to the approximation accuracy. 0 if precision is less
A second means for outputting an identifier indicating that the processing is completed, and if not, a second means for shifting to a third means to be described later. Third means for determining the node candidates of only the few nodes so as to be approximately equally spaced with respect to the index, and interpolating the node candidates by an interpolation function using an index number as an independent variable, A fourth means for calculating an error from the original one-dimensional time-series data; and calculating, from the error, a value of a first objective function defined by weighted addition of the maximum value of the error, the error average, and the error variance. Fifth means for repeating the change of the node candidate so as to minimize the value of the first objective function, and determining a sub-optimal node candidate; and By interpolation Seventh means for generating one-dimensional time-series data approximating the original one-dimensional time-series data, calculating an error between the one-dimensional time-series data and the original one-dimensional time-series data, Eighth means for calculating the value of the second objective function defined by weighted addition of the maximum value of the error, the average of the error, and the error variance, if the value of the second objective function is equal to or greater than a threshold value corresponding to the approximation accuracy For example, ninth means for repeating the processing from the third means to the eighth means by adding an increment to the number of nodes as a new number of nodes, and the value of the second objective function being less than the threshold value Then, tenth means for outputting compressed data composed of the initial time and time interval of the one-dimensional time-series data, the index number of the finally determined node candidate, and the value of the node candidate One-dimensional time-series data characterized by having Data compression device. 57. The one-dimensional time-series data compression device according to claim 52, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with a node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function If I (j-1) ≧ I (j) -1, set ΔE (1-) to 0, and if the relationship of I (j) +1 <I (j + 1) holds, Node candidate I
calculating the value of the first objective function when (j) is replaced with the node candidate I (j) +1, and calculating the original first value from the value of the first objective function.
Calculate a value ΔE (1+) obtained by subtracting the value of the objective function, and obtain I (j) + 1 ≧ I
If (j + 1), the ΔE (1+) is set to 0, and if the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is set. The node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j ) +1, if the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not exchanged, and the ΔE (1-) < 0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 is from small to large for odd j. The order of the objects and the even j are performed in ascending order from the largest to the smallest, and the value of the first objective function at the end of the series of processes is the value obtained by subtracting the threshold from the value of the original first objective function. Then, the above operation is performed again in the order of small to large for the odd j and in the order of large to small for the even j, and whether the node candidates have not been exchanged at all or the first objective function If the value is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, the processing is terminated to perform the one-dimensional time-series data compression apparatus. 58. The one-dimensional time-series data compression apparatus according to claim 53, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m, and if the relationship I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with a node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is established. If the above holds, the node candidate
The value of the first objective function when I (j) is replaced with the node candidate I (j) +1 is calculated, and the first first objective function is calculated from the value of the first objective function.
Calculate a value ΔE (1+) obtained by subtracting the value of the objective function, and obtain I (j) + 1 ≧ I
If the relationship (j + 1) holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is replaced with the node candidate I (j) -1, and if the relationship of ΔE (1-) ≧ 0 and the ΔE (1 +) <0 holds, the node candidate I (j) is replaced by the node If the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the ΔE ( 1-) <0 and the relationship of ΔE (1 +) <0 holds,
And, if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the The relation of ΔE (1 +) <0 holds,
And, if ΔE (1-) is larger than ΔE (1+), the operation of replacing the node candidate I (j) with the node candidate I (j) +1 is larger for odd j. From the smallest to the largest, and for even j, the smallest to the largest j, the value of the first objective function at the end of the series of processes is obtained by subtracting the threshold value from the value of the original first objective function. If it is less than the above, the above operation is performed again in the order of large to small for odd j and in the order of small to large for even j. If the value of the objective function is greater than the value obtained by subtracting the threshold value from the value of the original first objective function, the one-dimensional time-series data compression apparatus is performed by terminating the processing. 59. The one-dimensional time-series data compression apparatus according to claim 53, wherein the sub-optimal node candidate calculation is performed by numbering the index of the node candidate in ascending order. Are expressed as I (j), 0 ≤ j ≤ m, and if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j). −1, the value of the first objective function is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function is calculated. 1) ≧ I (j) -1
If the relationship holds, ΔE (1-) is set to 0. If the relationship I (j) +1 <I (j + 1) holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And, if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the The relation of ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+),
The operations of exchanging the node candidate I (j) for the node candidate I (j) +1 are from j = 1 to [m / 2] and j = m-1 to [m / 2] +1.
If the value of the first objective function at the end of the series of processes is equal to or less than the value of the original first objective function minus the threshold, the operation is performed from j = 1 to [m / 2] and j = m-
1 to [m / 2] +1 in order, and the node candidates are not exchanged at all, or the value of the first objective function is determined by subtracting a threshold value from the value of the original first objective function. A one-dimensional time-series data compression apparatus characterized in that the processing is completed by terminating the processing if it is larger. 60. The one-dimensional time-series data compression apparatus according to claim 53, wherein the sub-optimal node candidate calculation is performed by numbering indices of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m. If the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the relationship ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), an operation of replacing the node candidate I (j) with the node candidate I (j) +1
j = [m / 2] to 1 and j = [m / 2] +1 to m−1 in order, and the value of the first objective function at the time when these series of processes are completed is the first original function. If the value of the objective function is equal to or less than the value obtained by subtracting the threshold, the operation is performed from j = [m / 2] to 1 and j =
[M / 2] +1 to m-1 in order, and the exchange of the node candidates was not performed at all, or the value of the first objective function was obtained by subtracting a threshold value from the value of the original first objective function. A one-dimensional time-series data compression apparatus characterized in that the processing is terminated by completing the processing if it is larger than the one. 61. The one-dimensional time-series data compression apparatus according to claim 53, wherein the sub-optimal node candidate calculation is performed by numbering indices of the node candidates in ascending order. Is expressed as I (j), 0 ≤ j ≤ m. If the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the relationship ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), an operation of replacing the node candidate I (j) with the node candidate I (j) +1
j = 1 to m−1 in order, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value of the original first objective function minus the threshold, the operation is performed by j = 1 to m-1 again, and if the node candidates have not been exchanged at all, or if the value of the first objective function is greater than the value of the original first objective function minus a threshold value , A one-dimensional time-series data compression apparatus, which performs the processing by terminating the processing. 62. The one-dimensional time-series data compression apparatus according to claim 53, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. If the relation is expressed as I (j), 0 ≤ j ≤ m, then if the relation I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is If the relation of ΔE (1-) ≧ 0 and the relation of ΔE (1 +) <0 holds, the node candidate I (j) is replaced with the node candidate I (j). If the relationship ΔE (1-) ≧ 0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is not replaced, and the relationship ΔE (1-) <0 And the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the ΔE (1-) <0 and the ΔE (1 +) <0 holds,
If the ΔE (1-) is larger than the ΔE (1+), an operation of replacing the node candidate I (j) with the node candidate I (j) +1
j = m-1 to 1 in order, and if the value of the first objective function at the time when these series of processing is completed is equal to or less than the value of the original first objective function minus the threshold, the operation is performed by j = m-1 to 1 in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value , A one-dimensional time-series data compression apparatus, which performs the processing by terminating the processing. 63. The one-dimensional time-series data compression apparatus according to claim 53, wherein the sub-optimal node candidate calculation is performed by numbering indices of the node candidates in ascending order. Are expressed as I (j), 0 ≤ j ≤ m, and if the relationship of I (j-1) <I (j) -1 holds, the node candidate I (j) is replaced with the node candidate I (j). −1, the value of the first objective function is calculated, and a value ΔE (1-) obtained by subtracting the original value of the first objective function from the value of the first objective function is calculated. 1) ≧ I (j) -1
If the relationship holds, ΔE (1-) is set to 0. If the relationship I (j) +1 <I (j + 1) holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function and the value of the original first objective function at the time of performing the exchange, the ΔE (1-) ≧ 0 and the If the relationship of ΔE (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of this exchange and the element If the relationship of ΔE (1-) ≧ 0 and ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged, and the ΔE (1-) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) -1 and the first objective function when the exchange is performed. Is exchanged with the value of the original first objective function, and the relationship of ΔE (1-) <0 and ΔE (1 +) <0 holds,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first when this exchange is performed. The operation of exchanging the value of the objective function and the value of the original first objective function is performed in the order of small to large for odd j, and for even j
Are performed in the order from the largest to the smallest. If the value of the first objective function at the time when these series of processing is completed is equal to or less than the value obtained by subtracting the threshold from the value of the original first objective function, the operation is performed in an odd number. j is performed again in ascending order from small to large, and for even j, in ascending order from large to small. Whether the node candidates have not been exchanged at all, or the value of the first objective function is equal to the original first value A one-dimensional time-series data compression apparatus characterized in that if the value is larger than the value obtained by subtracting the threshold value from the value of the objective function, the processing is terminated to perform the processing. 64. The one-dimensional time-series data compression device according to claim 53, wherein the sub-optimal node candidate calculation is performed by numbering indices of the node candidates in ascending order. If the relationship is expressed as I (j), 0 ≤ j ≤ m, and if the relationship of I (j-1) <I (j) -1 holds, the node candidate I
The value of the first objective function when (j) is replaced with the node candidate I (j) -1 is calculated, and a value ΔE (1) obtained by subtracting the original value of the first objective function from the value of the first objective function is obtained. -), And if the relationship of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and I (j) +1
If the relationship <I (j + 1) holds, the value of the first objective function when the node candidate I (j) is replaced with the node candidate I (j) +1 is calculated. A value ΔE (1+) obtained by subtracting the value of the original first objective function from the value is calculated, and if the relationship of I (j) + 1 ≧ I (j + 1) holds, the above ΔE (1+) is calculated. 0, the node candidate I (j) is exchanged for the node candidate I (j) -1 if the relationship of ΔE (1-) <0 and ΔE (1+) ≧ 0 holds. The value of the first objective function at the time of this exchange and the value of the original first objective function are exchanged, and if the relationship of ΔE (1-) ≧ 0 and ΔE (1 +) <0 holds, The node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the value of the original first objective function are exchanged. 1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the node candidate I (j) is not exchanged. ΔE (1 -) <0 and the ΔE (1 +) <0 in relation holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
If the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is performed in the order of large to small for the odd j and in the order of small to large for the even j. If the value of the first objective function at the end of is less than or equal to the value of the original first objective function minus the threshold value, the operation is performed in the order of odd j, from large to small, and even j. Is performed again in ascending order from the smallest to the largest. If the node candidates are not exchanged at all, or if the value of the first objective function is larger than the value of the original first objective function minus a threshold value , By ending the process Determined series data compression apparatus when one-dimensional and performing. 65. The one-dimensional time-series data compression apparatus according to any one of claims 53 to 56, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. If the relation is expressed as I (j), 0 ≤ j ≤ m, then if the relation I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
If the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is from j = 1 to [m / 2
] And j = m-1 to [m / 2] +1, and the value of the first objective function when these series of processes are completed is obtained by subtracting the threshold value from the value of the original first objective function. If not, the operation is repeated again from j = 1 to [m / 2] and from j = m-1 to [m / 2] +1, and whether the exchange of node candidates has not been performed at all. If the value of the first objective function is larger than the value of the original first objective function minus a threshold value, the processing is terminated to make a decision. apparatus. 66. The one-dimensional time-series data compression device according to claim 53, wherein the sub-optimal node candidate calculation is performed by numbering indices of the node candidates in ascending order. If the relation is expressed as I (j), 0 ≤ j ≤ m, then if the relation I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) +1, and the first objective function at the time of the replacement is replaced. And the original first
The operation of exchanging the value of the objective function is performed in order from j = [m / 2] to 1 and from j = [m / 2] +1 to m−1. If the value of the objective function is equal to or less than the value of the original first objective function minus the threshold, the operation is performed from j = [m / 2] to 1 and j = [m / 2
+1 to m−1 in order, and if the node candidates have not been exchanged at all, or if the value of the first objective function is greater than the value of the original first objective function minus a threshold value For example, a one-dimensional time-series data compression apparatus characterized by performing the processing by terminating the processing. 67. The one-dimensional time-series data compression device according to any one of claims 53 to 56, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. If the relation is expressed as I (j), 0 ≤ j ≤ m, then if the relation I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
If the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is performed in order from j = 1 to m−1, and the value of the first objective function at the time when a series of these processes is completed is changed to the original value. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the first objective function, the above operation is performed again in order from j = 1 to m−1, and whether the exchange of the node candidates has not been performed at all or the value of the first objective function Is larger than the value obtained by subtracting the threshold value from the original value of the first objective function, by terminating the processing, thereby performing the one-dimensional time-series data compression apparatus. 68. The one-dimensional time-series data compression apparatus according to claim 53, wherein the calculation of the sub-optimal node candidates is performed by numbering indices of the node candidates in ascending order. If the relation is expressed as I (j), 0 ≤ j ≤ m, then if the relation I (j-1) <I (j) -1 holds, the node candidate I (j)
Is replaced with the node candidate I (j) -1, the value of the first objective function is calculated, and the value ΔE (1-) obtained by subtracting the value of the original first objective function from the value of the first objective function is obtained. If the relation of I (j-1) ≧ I (j) -1 holds, the above ΔE (1-) is set to 0, and the relation of I (j) +1 <I (j + 1) is satisfied. If this holds, the node candidate I
(j) is replaced with the node candidate I (j) +1, the value of the first objective function is calculated, and the value ΔE ((E) is obtained by subtracting the value of the original first objective function from the value of the first objective function. 1+), and I (j) + 1 ≧ I (j + 1)
If the relationship holds, the ΔE (1+) is set to 0.If the relationship ΔE (1-) <0 and the relationship ΔE (1+) ≧ 0 hold, the node candidate I (j) is Exchange with the node candidate I (j) -1 and exchange of the value of the first objective function at the time of the exchange and the value of the original first objective function are performed, and the ΔE (1-) ≧ 0 and the ΔE If the relationship of (1 +) <0 holds, the node candidate I (j) is exchanged for the node candidate I (j) +1, and the value of the first objective function at the time of the exchange and the original (1) After exchanging the value of the objective function, if the relationship of ΔE (1-) ≧ 0 and the relationship of ΔE (1+) ≧ 0 holds, the exchange of the node candidate I (j) is not performed; -) <0 and the relationship of ΔE (1 +) <0 holds,
And if the ΔE (1-) is equal to or less than the ΔE (1+), the node candidate I (j) is replaced with the node candidate I (j) -1, and the first objective function at the time of the replacement is replaced. The value and the value of the original first objective function are exchanged, and the relations of ΔE (1-) <0 and ΔE (1 +) <0 hold,
And if the ΔE (1-) is larger than the ΔE (1+), the node candidate I (j) is exchanged for the node candidate I (j) +1, and the first object at the time of the exchange is The operation of exchanging the value of the function and the value of the original first objective function is performed in order from j = m-1 to 1, and the value of the first objective function at the time when these series of processing is completed is changed to the original value. If the value is equal to or less than the value obtained by subtracting the threshold value from the value of the first objective function, the above operation is repeated again from j = m-1 to 1, and the exchange of the node candidates is not performed at all, or the value of the first objective function is determined. Is larger than the value obtained by subtracting the threshold value from the value of the original first objective function, by terminating the process,
A one-dimensional time-series data compression apparatus. 69. The one-dimensional time-series data compression apparatus according to claim 53, wherein if the finally determined number of node candidates is equal to or less than the number of non-candidate data, the node Compressed data composed of an identifier indicating a candidate, the index number of the finally determined node candidate, and the value of the node candidate is output, and if the finally determined number of node candidates is the candidate, If the number of the missing nodes is larger than the number of missing nodes, compressed data composed of an identifier that is not a node candidate, an index number of the data that did not become the node candidate, and a value of the node candidate is output. Series data compression device. 70. The one-dimensional time-series data compression apparatus according to claim 51, wherein said one-dimensional time-series data compression apparatus is used for one-dimensional time-series data with unequal intervals in time. A one-dimensional time-series data compression apparatus characterized in that time and data are applied independently and each is compressed independently. 71. The one-dimensional time-series data compression apparatus according to claim 51, wherein each of the plurality of one-dimensional time-series data constituting the multi-dimensional time-series data is compared with the one-dimensional time-series data. A one-dimensional time-series data compression apparatus characterized in that multi-dimensional time-series data is compressed by repeatedly applying a data compression apparatus. 72. The one-dimensional time-series data compression apparatus according to claim 51, wherein the one-dimensional time-series data in which a plurality of errors propagate is obtained from the one-dimensional time-series data of a propagation source. A one-dimensional time-series data compression apparatus characterized in that all the one-dimensional time-series data are compressed by sequentially increasing the approximation accuracy value and repeatedly applying the one-dimensional time-series data compression apparatus. 73. An apparatus for decompressing compressed data compressed by the one-dimensional time-series data compression apparatus according to claim 51, wherein the compressed data and the decompressed compressed data are decompressed. First means for inputting the number of data of the compressed data and the same interpolation function as the interpolation function used for the compression are used to interpolate the compressed data to calculate the same number of data as the number of data. And second means for calculating a time from the time interval by the same number as the number of data, and third means for outputting the data and the time calculated by the second means. A one-dimensional time series data decompression device. 74. An apparatus for decompressing compressed data compressed by the one-dimensional time-series data compression apparatus according to claim 52, wherein the compressed data and the compressed data are decompressed. First means for inputting the number of data, and when an identifier indicating that the data is all 0 is added to the compressed data, 0 for the same number as the number of data, initial time and time interval From the same number as the number of data, and if the compressed data does not have an identifier indicating that the data is all 0, use the same interpolation function as that used for compression. Interpolating the compressed data to calculate the same number of data as the number of data, and calculating the time from the initial time and the time interval by the same number as the number of data, the second means, Before calculated by A one-dimensional time-series data decompression device, comprising: third means for outputting the data and the time. 75. The one-dimensional time-series data decompression device according to claim 73, wherein each of the plurality of compressed one-dimensional time-series data forming the compressed multi-dimensional time-series data is subjected to the one-dimensional time-series data. A one-dimensional time-series data decompression apparatus characterized in that compressed multi-dimensional time-series data is decompressed by repeatedly applying a time-series data decompression apparatus.