JP2006031378A - Apparatus for complementing time-series data, its method, and its program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an apparatus for complementing time-series data that smoothly complements time-series data having missing data, its method, and its program. <P>SOLUTION: The apparatus 1 for complementing time-series data uses a data input means 20 to write time-series data having missing data into a storage means 10, and uses a data complementing means 40 to create complement data with an interpolation function that corresponds to the number of actual data inputted at least either before or after missing data on a time series within a predefined time section. The complement data is written in the storage means 10. A data output means 30 reads the complemented complement data or actual data in time series from the storage means 10 and outputs the data. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a time-series data complementing device that complements missing data in time-series data, a method thereof, and a program thereof.

  Conventionally, when handling data input in time series, the data value of missing data at any point in time, or the data value at the sampling point where data originally does not exist, is complemented, A complementary technique for generating a data value at an arbitrary time is disclosed (Patent Document 1, Patent Document 2, etc.).

  For example, in the complementary technique disclosed in Patent Document 1, attention is paid to the frequency characteristics of actual data in the time-series data of pixel signals obtained from the output of a solid-state imaging device as video signals, and sinc is applied to peripheral pixel signals. A signal between pixels is generated by using a function (interpolation function).

In addition, for example, in the complementing technique disclosed in Patent Document 2, when complementing a point cloud in an N-dimensional space, it is represented by a polynomial from a scalar quantity and a spatial differential coefficient that are known information in advance. The coefficient of the interpolation function is determined, and the scalar quantity and the spatial differential coefficient at an arbitrary point in the N-dimensional space are obtained by the interpolation function.
In the present specification, “interpolation” and “complement” are distinguished from each other as follows. That is, “interpolation” means that data between the data and data outside the data is generated by interpolation or extrapolation, and is used only for the interpolation function here. In addition, “complement” means to complete the data by supplementing the value for missing data or non-existing data. For example, the missing data or the like is obtained by the value obtained by the interpolation function. Used when supplementing.
JP-A-5-145934 (paragraphs 0016 to 0021, FIG. 6) JP 9-319731 A (paragraphs 0021 to 0024, FIG. 6)

  However, in the conventional complementary technique, for example, in the technique disclosed in Patent Document 1, when missing data is generated based on the same interpolation function, missing data is unequal, for example. In the case of occurrence at intervals, since all unequal intervals cannot be expressed by the same interpolation function, there is a problem that appropriate data cannot be generated.

  Further, in the technique disclosed in Patent Document 2, missing data is complemented by an interpolation function having different coefficients. However, a temporal change (a certain time) of actual data used to supplement missing data is performed. Therefore, there is a problem in that appropriate data is not generated because the optimum interpolation function is not always applied.

  Thus, in the conventional complementary technology, for example, when the time-series data is data indicating the trajectory of the pitched ball, the trajectory shape between the initial trajectory of the ball and the trajectory of the ball immediately before the fall Despite the difference, since interpolation is performed without considering one type of interpolation function or considering temporal changes in actual data, appropriate data is not generated for missing data and smooth interpolation is performed. There is a problem that can not be.

  The present invention has been made to solve the above-described problems. In time-series data with missing data, an interpolation function is adaptively applied to temporal changes in actual data existing in the vicinity of the missing data. It is an object of the present invention to provide a time-series data complementing apparatus, a method thereof, and a program thereof capable of performing smooth complementation by changing the values.

  The present invention was created to achieve the above object. First, the time-series data complementing apparatus according to claim 1 inputs time-series data lacking data, and is an actual time-series data. A time-series data complementing device that complements missing data based on data, and includes a storage unit, a data input unit, a data complementing unit, and a data output unit.

  According to such a configuration, the time series data complementing device inputs time series data by the data input means, and sequentially writes the time series data in the storage means in time series. This time-series data is a data string in which data is irregularly lost, and the actual data is sequentially written in the storage means, but since the missing data is not written, it is stored in the storage means in a data missing state. Will be. This missing data has a strong correlation with the temporal change of the actual data preceding and following the data (the number of actual data within a certain time, the distance of the actual data from the missing data, etc.).

  Therefore, the time series data complementing device performs interpolation corresponding to the number of actual data input before or after the missing data on the time series within a predetermined time interval by the data complementing means. A function is used to supplement missing data and generate supplementary data. Then, the data complementing means writes the interpolation data in the storage means. It should be noted that the interpolation function may be determined by determining the degree and coefficient of the polynomial according to the number of actual data within a predetermined time interval, or by preparing a plurality of interpolation functions in advance. As a result, the missing data can be complemented in accordance with temporal changes in the actual data before and after.

  Then, the time series data complementing device reads the time series data from the storage means in time series by the data output means and outputs it. Note that the time-series data stored in the storage means is such that the missing data is supplemented with the supplemental data, so that the output data is continuous time-series data without any missing data.

  According to a second aspect of the present invention, there is provided the time series data complementing apparatus according to the first aspect, wherein the data complementing means includes a supplementary interval extracting means, an actual data counting means, and an interpolation function determining means. And a complementary data generation means and a data update means.

According to such a configuration, the time-series data complementing device extracts a supplemental section lacking data from the time-series data stored in the storage unit by the supplementary section extracting unit. This complementary section is regarded as one section when missing data is continuous.
The supplementary section in which one or more missing data is continuous has a strong correlation with the temporal change of the actual data that precedes and follows the time series of the supplementary section.
Therefore, the time-series data complementing apparatus is configured so that the actual data counting unit counts the number of actual data in a predetermined time interval at least before or after the supplemental interval extracted by the supplementary interval extraction unit. The interpolation function is determined by the interpolation function determination means based on the number of actual data and the value of the actual data.

Then, the time-series data complementing device generates complementing data that complements the missing data in the complementing section based on the interpolation function determined by the interpolation function determining unit by the complementing data generating unit. As a result, the complementary data becomes data adapted to the temporal change of the actual data before and after. Even if the missing data is continuous, complementary data is generated in the section using the same interpolation function.
Then, the time-series data complementing device updates the time-series data stored in the storage unit by complementing the missing data with the complement data generated by the supplement data generation unit by the data updating unit. As a result, the time series data stored in the storage means becomes continuous time series data with no omission.

  Furthermore, the time-series data complementing apparatus according to claim 3 is the time-series data supplementing apparatus according to claim 1 or 2, wherein the data input means stores the time-series data in time series in the storage means. When writing, the time-series data is written in an area shifted in the past by a predetermined delay time.

  According to such a configuration, the time series data complementing device writes the input data in the data input unit in the area shifted in the past by the predetermined delay time of the storage unit, so the data read by the data output unit is On the contrary, future data is read by the delay time with respect to the written data. As a result, the time-series data complementing device complements future data with respect to the input data.

  The time-series data complementing apparatus according to claim 4 is the time-series data complementing apparatus according to any one of claims 1 to 3, wherein the data output means is time-series from the storage means. When reading the time-series data, the time-series data is read from an area shifted in the past by a predetermined delay time.

According to such a configuration, the time-series data complementing apparatus reads out the data to be output from the area shifted in the past by the predetermined delay time of the storage unit in the data output unit. The past data is sequentially output.
By changing the delay time in the data output means and the delay time in the data input means, the time series data complementing device can output time series data of an arbitrary time with respect to the current time.

  Furthermore, the time-series data complementing method according to claim 5 is a time-series data complementing method for inputting time-series data lacking data and complementing the missing data based on actual data that is the time-series data. And a data input step, a data complement step, and a data output step.

  According to this procedure, in the time series data complementing method, in the data input step, time series data is input, and the time series data is sequentially written in the storage means in a time series. This time-series data is a data string in which data is irregularly lost, and the actual data is sequentially written in the storage means, but since the missing data is not written, it is stored in the storage means in a data missing state. Will be.

Then, the time series data complementing method is an interpolation corresponding to the number of actual data input before or after the missing data on the time series within a predetermined time interval in the data complementing step. Complement data that complements the missing data is generated by the function, and the supplement data is written to the storage means. As a result, the missing data can be complemented in accordance with temporal changes in the actual data before and after.
In the time series data complementing method, in the data output step, the time series data is read from the storage means in time series and output. Note that the time-series data stored in the storage means is continuous time-series data with no omission because the missing data is complemented with the complement data.

  The time-series data supplement program according to claim 6 inputs time-series data lacking data, and inputs data to the computer in order to supplement the missing data based on the actual data that is the time-series data. Means, supplementary interval extracting means, actual data counting means, interpolation function determining means, complementary data generating means, data updating means, and data output means.

According to such a configuration, the time series data complementing program inputs time series data by the data input means, and sequentially writes the time series data to the storage means in time series.
Then, the time series data complementing program extracts the supplementary section lacking data from the time series data stored in the storage means by the supplementary section extracting means, and the actual data counting means at the time of the supplementary section. The number of actual data in a predetermined time interval is measured at least either before or after the series. Further, the time series data complementing program determines the interpolation function based on the number of actual data and the value of the actual data by the interpolation function determining means.

  Then, the time series data complementing program generates complementing data that complements the missing data in the complementing section based on the interpolation function determined by the interpolation function determining unit by the complementing data generating unit. As a result, the complementary data becomes data adapted to the temporal change of the actual data before and after.

  Further, the time series data supplement program updates the time series data by supplementing the missing data in the storage means with the supplement data generated by the supplement data generation means by the data updating means. As a result, the time series data stored in the storage means becomes continuous time series data with no omission. Then, the time series data complementing program reads out the time series data from the storage means in time series by the data output means and outputs it.

  According to the invention described in claim 1 or claim 5, even if time-series data is missing, each missing data is complemented by changing the interpolation function based on the temporal change of the preceding and following actual data. Therefore, it is possible to perform smooth complementation on the missing data. Further, the present invention complements data using different interpolation functions even when data loss occurs at unequal intervals or occurs continuously in time-series data. Therefore, it is possible to perform smooth and complete complementation.

  According to the invention described in claim 2 or claim 6, when data missing in time-series data is extracted as a complementary section and an interpolation function is determined for each section, data is continuously missing The missing data is interpolated by the same interpolation function. This can reduce the amount of calculation when performing the complementing process.

According to the third aspect of the present invention, it becomes possible to supplement future data with respect to the input data.
According to the fourth aspect of the present invention, it is possible to sequentially output past data for the input data.

  Thus, according to the present invention, it is possible to input data at an arbitrary time and output data at an arbitrary time as long as it is within a certain time range. Thus, for example, when the position where the ball has moved in the video is acquired as time-series data, the present invention generates a video effect such as drawing the trajectory of the ball after a certain time after the movement of the ball. It can be used for.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
[Configuration of time-series data complementing device]
First, the configuration of the time-series data complementing device according to the present invention will be described with reference to FIG. FIG. 1 is a block diagram showing a configuration of a time-series data complementing apparatus.
As shown in FIG. 1, the time-series data complementing apparatus 1 inputs time-series data and complements the missing data in the time-series data. Here, the time-series data complementing apparatus 1 includes a storage unit 10, a data input unit 20, a data output unit 30, and a data complementing unit 40.

The storage means 10 stores time-series data input by the data input means 20 described later in association with at least an attribute indicating whether it is missing data or actual data, and is stored in a memory (RAM: Random). (Access Memory) or a storage device such as a hard disk.
Here, the configuration of data stored in the storage unit 10 will be described with reference to FIG. FIG. 2 is a block diagram showing the arrangement structure of data stored in the storage means.
Here, the structure of the data stored in the storage means 10 is an array structure having N elements whose addresses Ad are “0” to “N−1”. Specifically, the storage unit 10 includes a data area Da having arrays D [0] to D [N−1] for storing numerical values of data, and arrays A [0] to A [N] for storing data attributes. -1] and the attribute area Aa.
The data stored in the data area Da is actual data (actual data) input from the data input unit 20 or supplemented data supplemented by the data supplementing unit 40 described later.

In addition, the attribute stored in the attribute area Aa indicates whether the data stored in the data area Da is not stored, actual data is stored, or complementary data is stored. It is information indicating whether or not the state is present. Here, “0” is stored when the data stored in the data area Da represents a state where data is not stored (missing data), “1” is stored when actual data is stored, and complementary data is stored. In this case, the numerical value “2” is stored in the attribute area Aa as an example.
Further, hereinafter, the content (data value) of the data area Da having the address Ad of n (n = 0, 1,..., N−1) is D [n], and the content (attribute value) of the attribute area Aa. This is expressed as A [n].
It is assumed that the attribute area Aa of the storage unit 10 is initialized with an attribute value (for example, “0”) indicating that it is not actual data by an initialization unit (not shown).
Returning to FIG. 1, the description will be continued.

The data input means 20 inputs time series data from the outside. The data input here is sequentially written into the storage means 10.
Here, the data input unit 20, at the current time t (a non-negative integer value of t in later), the data value at e unit time past than t from the outside, i.e. the time (t-e) D _in (t -E) is input. The retroactive amount e, which is a delay time from the current time t, is an integer of 0 ≦ e <N (N is the number of array elements in the storage means 10 (see FIG. 2)). The retroactive amount e will be further described later.

In addition, when the data value D _in (te) is input, the data input means 20 writes the data value D _in (te) in the data area Da of the storage means 10 and at the same time the attribute area Aa. The attribute value indicating that it is actual data is written in. Note that the write destination address w in the storage means 10 is, for example, an address obtained by the calculation shown in the following equation (1). Here, (mod N) indicates a remainder when dividing by N.

As a result, the data input means 20 uses the addresses “0” to “N−1” in the storage means 10 in a ring shape.
Then, the data input means 20 uses the data value D _in (te) and the attribute indicating the actual data, as shown in the following expression (2), for the address w calculated in the expression (1). Write the value “1”.

  In addition, when no data is input at the current time t (missing data), the data input means 20 writes an attribute value indicating that the data is not actual data (missing data) in the attribute area Aa of the storage means 10. For example, when the address of the write destination in the storage means 10 is the address w in the above expression (1), the data input means 20 can store missing data with respect to the address w as shown in the following expression (3). The indicated attribute value “0” is written. At this time, the data value is an arbitrary value.

  Then, as shown in the equations (2) and (3), the data input means 20 sends a notification “write completion notice” to the data complementing means 40 at the stage of writing the data in the storage means 10. Notice.

  The data output means 30 sequentially reads actual data or complementary data that is time-series data stored in the storage means 10 and outputs it to the outside. The data output unit 30 outputs data (actual data or supplemental data) every time a notification “completion completion notification” indicating completion of missing data completion is notified from the data supplementing unit 40 described later. .

Further, the data output means 30 reads out and outputs the data value D _out (td) at the d unit time past from the current time t, that is, the time (td), from the storage means 10. The retroactive amount d, which is a delay time from the current time t, is an integer of 0 ≦ d <N (N is the number of array elements in the storage means 10 (see FIG. 2)). How to use the retroactive amount d will be described later.

  Further, the address r when the data output means 30 reads the data in the storage means 10 is, for example, an address obtained by the calculation shown in the following equation (4). Here, (mod N) indicates a remainder when dividing by N.

Then, as shown in the following equation (5), when the attribute value A [r] at the address r is the attribute value “0” indicating missing data, the data output means 30 is not a number (NaN: Not a Number) is output as the data value D _out (t−d), and for other attribute values, the data value D [r] is output as the data value D _out (t−d).

Here, it is assumed that the attribute value A [r] is an attribute value “0” indicating missing data. However, when data complementing means 40 described later operates, data is lost for a long time. Except for, missing data is complemented and changed to complemented data (attribute value “2”).
Note that the data output means 30 replaces the data value D [r] and the attribute value A [r] at the address r with the time (as shown in the following expression (6) instead of the expression (5), respectively. It is good also as outputting as data value _Dout (td) and attribute value _Aout (td) in td).

Here, with reference to FIG. 3 (refer to FIG. 1 as appropriate), the relationship between the data writing to the storage means 10 performed by the data input means 20 and the data reading from the storage means 10 performed by the data output means 30 will be described. . FIG. 3 is an explanatory diagram for explaining the relationship between data writing and reading in the array stored in the storage means.
Here, the array of the data area Da corresponding to the addresses “0” to “N−1” of the storage means 10 is D [0] to D [N−1], and the array of the attribute area Aa is A [0] to A. It is assumed that [N−1] and the data value and attribute value corresponding to the current time t are written in the area (D [i] and A [i]) corresponding to the address “i”.

Here, when data e unit time past from the current time t is input to the data input means 20, the data input means 20 calculates the write address “w” by the above equation (1) (here w = i). -E), and as past data delayed by e unit time, the data value is written in the array D [ie] and the attribute value is written in the array A [ie].
Further, the data input means 20 reads past data delayed by d unit time from the current time t from the storage means 10. That is, the data input means 20 calculates the read address “r” by the above equation (4) (here, r = id), and reads D [id] that is a data value in the past d unit time.

Here, the retroactive amount e which is the delay time from the current time t of the data input to the data input means 20 and the retroactive amount d which is the delay time from the current time t when the data output means 30 outputs are set. How to use is explained.
For example, when the relationship “retroactive amount e <retroactive amount d” is satisfied, the data value D _out (t−d) of the data output from the data output means 30 (the value of D [id] in FIG. 3) Is past information relative to the data value D _in (te) of the data input to the data input means 20 (value of D [ie] in FIG. 3).

When the relationship of “retroactive amount e = retroactive amount d” is satisfied, the data value D _out (t−d) of the data output from the data output means 30 is the data of the data input to the data input means 20. It becomes information at the same time relative to the value D _in (te).
When the relationship of “retroactive amount e> retroactive amount d” is satisfied, the data value D _out (t−d) of the data output from the data output means 30 is the data of the data input to the data input means 20. It becomes information of the future relative to the value D _in (te).

  As described above, the time-series data complementing apparatus 1 can input information at an arbitrary time and output information at an arbitrary time as long as 0 ≦ e <N and 0 ≦ d <N are satisfied. Note that the retroactive amount e and the retroactive amount d may be set in advance as constants in the data input means 20 and the data output means 30, or may be set as variables from the outside.

For example, by tracking the soccer ball by changing the retroactive amount e and the retroactive amount d, and the trajectory can be acquired as time-series data, even if the video at the moment of shooting is not displayed on the screen, When the screen is switched to the shooting scene, the trajectory of the ball from the moment when the shooting is performed by tracing back the time series data can be acquired. As a result, the trajectory of the ball from the moment of shooting can be displayed on the screen. Further, when it is possible to acquire a hit ball trajectory in baseball as time series data, a future ball trajectory can be displayed on the screen by setting e> d.
Returning to FIG. 1, the description will be continued.

  The data complementing means 40 is time-series data stored in the storage means 10 and supplements missing data by changing the interpolation function based on actual data at least before or after the missing data. The data complementing means 40 operates when there is a notification “writing completion notice” indicating that data has been written from the data input means 20 to the storage means 10. Here, the data complementing means 40 includes a complementing section extracting means 41, a complementing means 42, and a data updating means 43.

  The complementary section extracting unit 41 refers to the attribute value of the time-series data stored in the storage unit 10 and detects the presence or absence of actual data, thereby extracting a complementary section for complementing the missing data. is there.

  The supplementary section extracting means 41 searches for a predetermined number of actual data to find out how many hours past the actual data is from the current time t, and extracts a section between the actual data as a supplementary section. The extracted supplementary section is notified to the supplementing means 42. Note that the complementary section extracting unit 41 notifies the complementary unit 42 of the actual data value at the same time.

  Here, with reference to FIG. 4 (refer to FIG. 1 as appropriate), the complementary section extracted by the complementary section extraction means 41 will be described. FIG. 4 is an explanatory diagram for explaining the concept of a supplementary section, where (a) shows input time-series data with missing parts, and (b) shows a supplementary section extracted from the time-series data. An example is shown.

In FIG. 4A, time-series data with missing data written from the data input means 20 to the storage means 10 is schematically shown, and the right side shows past data. In FIG. 4, the ◯ mark indicates missing data (missing data), and the ● mark indicates actual data.
At this time, the complementary section extracting means 41 sequentially searches the retroactive amount (value indicating how many unit time the past data) exists in the actual data from the current time t to the past. Then, the retroactive amount u (T _R [s]) when the s-th actual data exists from the current time t is extracted.

For example, as shown in FIG. 4B, the supplementary interval extracting unit 41 sets the retroactive amount T _R [0] = 1 when the 0th actual data from the current time t is data that is one unit time past. In the case where the first actual data is data of 4 unit times in the past, the retroactive amount T _R [1] = 4. In this way, the complementary section extraction unit 41 sequentially searches the retroactive amount T _R [s].
At this time, the complementary section extraction unit 41 extracts the data value (D _R [s]) of the s-th actual data from the current time t.

It is assumed that the complementary section extracting unit 41 does not perform retroactive exceeding a predetermined maximum retroactive amount N _lim (0 ≦ N _lim <N: N is the number of data arrays stored in the storage unit 10). In addition, the complementary section extraction unit 41 does not perform the subsequent search when the predetermined number of actual data S is searched. In this case, the number of the actual data, when was S'number less than S passed, complementary section extracting means _{41, T R [S'] = T} R [S'+ 1] = ... = T R [S-1] = N _lim +1 is set.
Based on each retroactive amount T _R [s] (s = 0, 1,..., S−1) extracted (set) in this way, as shown in the following equation (7), (S + 1) By setting the sections U _{0 to} U _S as open spaces, it is possible to represent a missing data section, that is, a complementary section.

In the set sections U _{0 to} U _S , as shown in FIG. 4B, a section in which missing data is continuous becomes one section. Since this section is an open section and a set of integers, the missing data is empty (empty set φ) in a region where actual data continues (for example, U ₂ in FIG. 4B).
Returning to FIG. 1, the description will be continued.

The complementing means 42 supplements the missing data for each of the supplementary sections (sections U _{0 to} U _S ) extracted by the supplementary section extracting means 41 based on actual data existing at least before or after the section to be supplemented. Is to do. Note that the complementing unit 42 notifies the data output unit 30 of a completion notification without performing the complementing process when all sections are empty sets φ, that is, there is no missing data.
Here, the complementing means 42 includes an actual data counting means 42a, an interpolation function determining means 42b, and a complementary data generating means 42c.

The actual data counting means 42a measures the number of actual data existing in a predetermined time section before and after the time series of the sections to be complemented extracted by the supplementary section extracting means 41. The number of actual data measured by the actual data counting unit 42a is output to the interpolation function determining unit 42b. Here, the actual data counting means 42a determines the number of actual data, the number N _{before of the} actual data previously input in time series with respect to a certain section U _s to be complemented, and the section U _s. respect, when measured by dividing into the number N _after the actual data inputted later in series.

The number N _after (s) of actual data input after this section U _s is a retroactive amount smaller than the lower limit value (inf (U _s )) of the section U _s , as shown in the following equation (8). d _after ), the number of elements (s) of the set consisting of elements (retroactive amounts) having an attribute value “1” existing in 0 <d _after <inf (U _s ).

On the other hand, the number N _before (s) of the actual data input before the interval U _s, as shown in the following equation (9), larger than the upper limit value of the interval U _s (sup (U _s)) retrospectively The quantity (assumed to be d _before ) is the number of elements in the set composed of elements (retroactive quantities) having an attribute value “1” existing in sup (U _s ) <d _before ≦ N _lim .

That is, actual data counting unit 42a, the equation (8) and (9) by measuring the number of elements in formula, to measure the number of actual data in the time interval 0 to N _lim.

The interpolation function determining unit 42b is an interpolation function for complementing missing data in the section based on the number of real data before and after the section to be complemented and the data value measured by the actual data counting unit 42a. Is to determine.
Hereinafter, an example in which the interpolation function determining unit 42b determines a polynomial interpolation function will be described.
Here, the interpolation function determining means 42b determines the interpolation function P (u) by a K-th order polynomial shown in the following equation (10) based on the number of actual data before and after the section to be complemented. And

Then, the interpolation function determining means 42b determines the degree K and the coefficient a _k (k = 0, 1,..., K) of the interpolation function P (u) by the polynomial shown in the equation (10).
For example, the interpolation function determining unit 42b, in a certain section U _s, orders the retroactive amount is subtracted from the "0" N _lim number of actual data present in the (maximum retroactive amount) (total) "1" value K And In this case, the interpolation function determination means 42b has N _after (s) (refer to equation (8)) and N _before (s) (refer to equation (9)) which are the numbers of actual data input before and after the section U _s . ) And the order K is calculated by the following equation (11).

When both N _after (s) and N _before (s) are “0” and the value of the order K is “−1”, the interpolation function determination unit 42b does not determine the interpolation function, It is assumed that no complement processing is performed on the section U _s .
Then, the interpolation function determining means 42b calculates the coefficients a _k (k = 0, 1,..., K) by matrix calculation shown in the following equation (12). T _R (k) (k = 0, 1,..., K) indicates the retroactive amount when the k-th actual data exists from the current time set by the complementary section extracting means 41. Furthermore, D _R (k) (k = 0, 1,..., K) indicates the value of actual data in the retroactive amount T _R (k).

As a result, the interpolation function P (u) of the equation (10) becomes a K-th order polynomial passing through all points (K + 1) of the actual data when the actual data is a point sequence. Then, by using this interpolation function P (u), it is possible to calculate the value of the missing data in the complementary data generation means 42c described later.
Here, the interpolation function determination unit 42b calculates the degree K by (actual data number −1) as shown in the above equation (11), but as shown in the following equation (13), The order K may be limited by the determined maximum order _Kmax .

Again, if the value of order K becomes "-1", the interpolation function determining unit 42b does not determine the interpolation function, and is not performed complementary processing for interval U _s.
Further, the interpolation function determination unit 42b calculates the coefficient of the polynomial based on the value of the actual data within the predetermined maximum retroactive amount, going back to the past from the current time, as shown in the equation (12). However, the actual data used for the calculation may be limited to the vicinity of the complementing section to be complemented.

Maximum example, the interpolation function determining means 42b from the side close to the section U _s at the side retroactive amount is smaller than the interval U _s up to M _after pieces, from the side close to the section U _s at the side retroactive amount is larger than the interval U _s Use up to M _before actual data. Here, it is assumed that L pieces of actual data in the vicinity of the complement section to be complemented and the retroactive amount up to a certain point of each real data are b _{0 to} b _L−1 . The order K is a small value between a predetermined maximum order K _max and (L−1), as shown in the following equation (14).

In this case, the interpolation function determination means 42b calculates the coefficient a _k (k = 0, 1,..., K) by the matrix calculation shown in the following equation (15). T _R (k) (k = b ₀ , b ₁ ,..., B _L-1 ) is a retroactive amount when the k-th actual data from the current time set by the complementary section extracting means 41 exists. Indicates. Further, D _R (k) (k = b ₀ , b ₁ ,..., B _L-1 ) indicates the value of actual data in the retroactive amount T _R (k).

The complementary data generation unit 42c generates complementary data for complementing the missing data by synthesizing the actual data using the interpolation function determined by the interpolation function determination unit 42b.
Here, focusing on the interval U _s to be complemented, when the interpolation function is P (u), the complement data value D _ins (j) at a time retroactive by j∈U _s from the current time is D _ins (j ) = P (j). Therefore, the complementary data generation unit 42c generates complementary data by using an interpolation function for all the complementary sections to be complemented.
Then, the complementary data generation unit 42 c outputs the complementary data and the retroactive time (retroactive amount) when the complementary data is generated to the data update unit 43.

The data updating unit 43 updates the missing data to the complementary data by writing the complementary data generated by the complementary data generating unit 42c of the complementing unit 42 into the storage unit 10. The data updating means 43 writes the complementary data in the data area of the storage means 10 based on the retroactive time output from the complementary data generating means 42c, and confirms that the data is the complementary data in the attribute area. The indicated attribute value “2” is written.
That is, when the value of the complementary data in the retroactive amount j of time is D _ins (j), the data update unit 43 stores the value of the data area as shown in the following equation (16). And write the value of the attribute area.

Here, t is the current time, N is the number of array elements in the storage means 10, and (mod N) is the remainder when dividing by N.
Then, the data update unit 43 notifies the data output unit 30 of a notification “completion completion notification” to the effect that the completion of the missing data is completed. As a result, the data output means 30 can output the time-series data that has been sequentially complemented.

As described above, by configuring the time-series data complementing apparatus 1, even if there is missing data in time-series data that is sequentially input in time series, at least before or after the missing data. Complementary data can be generated based on the data.
In addition, the time-series data complementing apparatus 1 generates the supplemental data by changing the interpolation function according to the temporal change of the actual data existing in the vicinity of the missing data, so that the real data can be complemented smoothly. It becomes possible.

  Note that the time-series data complementing apparatus 1 can also be realized as a time-series data complementing program that causes a general computer to function as each of the above-described means. This time-series data supplement program can be distributed via a communication line, or can be distributed by writing on a recording medium such as a CD-ROM.

[Operation of time-series data complementer]
Next, the operation of the time-series data complementing apparatus according to the present invention will be described with reference to FIG. 5 (refer to FIG. 1 as appropriate). FIG. 5 is a flowchart showing the overall operation of the time-series data complementing apparatus.

(Initialization step)
First, the time-series data complementing apparatus 1 initializes a write address and a read address for the storage unit 10 by an initialization unit (not shown) and sets an initial value in the attribute area (step S1).

  Note that an initialization unit (not shown) initializes the write address and the read address by shifting a predetermined retroactive amount with respect to the current time. Further, the initialization unit performs initialization by writing an attribute indicating that it is not “real data” in the attribute area of the storage unit 10. In this way, by initializing the write address and the read address by shifting them in advance by the retroactive amount from the current time, it becomes possible to input data at any time and output data at any time Become.

(Data entry step)
After this initialization, the time-series data complementing apparatus 1 sequentially inputs data from the outside by the data input means 20 (step S2).
Then, when real data is input, the time-series data complementing device 1 writes the value of the actual data in the data area of the storage means 10 and the attribute value indicating the actual data in the attribute area (for example, “1”). ) Is written. Further, when no actual data is input, the time-series data complementing apparatus 1 writes an attribute value (for example, “0”) indicating that the data is not actual data (missing data) in the attribute area of the storage unit 10. (Step S3).

(Data completion step)
Thereafter, the time-series data complementing device 1 detects the presence or absence of actual data by referring to the attribute value of the time-series data stored in the storage unit 10 by the supplementary interval extracting unit 41 of the data complementing unit 40. Then, a supplementary section for complementing the missing data is extracted (step S4). The operation of extracting the complementary section (step S4) will be described in detail later.

  Next, the time series data complementing apparatus 1 exists in a predetermined time section before and after the time series of the section (complement section) to be complemented extracted in step S4 by the actual data counting section 42a of the complement section 42. The number of actual data to be measured is measured (step S5). The value of the data to be complemented in the section to be complemented has a strong correlation with the number of actual data existing before and after the section.

  Therefore, the time-series data complementing apparatus 1 determines an interpolation function for calculating the value of missing data based on the number of actual data measured in step S5 by the interpolation function determination unit 42b (step S6). In this step S6, when the interpolation function is a polynomial, the coefficient is expressed as a retroactive amount from the current time until the actual data exists, as shown in the equation (12) or the equation (15). By making a decision based on the actual data value, smoother complementation is possible.

Then, the time-series data complementing apparatus 1 calculates the missing data value of the section to be complemented by the interpolation function determined in step S6 by the complement data generating unit 42c, and generates the complement data (step S7). .
Then, the time-series data complementing apparatus 1 writes the supplementary data generated in step S7 into the data area of the storage unit 10 by the data updating unit 43, and also indicates an attribute value (for example, the supplementary data in the attribute region) "2") is written (step S8).

(Data output step)
In this way, at the stage where the complementary data is written in the storage means 10, the time series data complementing apparatus 1 reads and outputs the data from the current read address by the data output means 30 (step S9).
Thereafter, the data input means 20 and the data output means 30 update the write address and the read address for the storage means 10 (step S10).

  Then, the data input means 20 determines whether or not data is continuously input (step S11). If the data is continuously input (Yes), the process returns to step S2 to continue the complementing operation. On the other hand, when the data is not continuously input (No), the time series data complementing apparatus 1 ends the operation. Note that the determination in step S11 determines that data is no longer input, for example, when missing data continues for a predetermined time or more.

  As described above, when time-series data having a missing part is input by operating the time-series data complementing apparatus 1, the time-series data complementing apparatus 1 changes the interpolation function based on the actual data before and after the missing part. To generate complement data for the missing portion. As a result, the time-series data complementing apparatus 1 can output time-series data with no omission.

(Extraction period extraction operation)
Next, referring to FIG. 6 (refer to FIG. 1 as appropriate), the operation of the complementary section extracting means 41 (the operation in step S4 in FIG. 5) will be described in detail. FIG. 6 is a flowchart showing an operation of extracting a complementary section performed by the complementary section extracting unit.

First, the supplementary interval extracting means 41 is a predetermined array of actual data, S _R [0], T _R [1],..., T _R , representing the retroactive amount of actual data from the current time. [S-1] is initialized. Here, initialization is performed by substituting a predetermined maximum retroactive amount N _lim for the elements of each array.

Further, the complementary section extraction unit 41 initializes a data index s indicating an index of actual data from the current time (value “0”), and further initializes a retroactive amount i from the current time (value “0”). (Step S41).
Then, the complementary section extraction unit 41 refers to the attribute area of the storage unit 10 and determines whether the i-th attribute value of the attribute area is “1” (actual data) (step S42).

If the i-th attribute value in the attribute area is not “1” (No in step S42), the process proceeds to step S46.
On the other hand, when the i-th attribute value of the attribute area is “1” (Yes in step S42), the complementary section extraction unit 41 sets i, that is, a retroactive amount in the array T _R [s]. In addition, the value of actual data at this time is set to D _R [s]. Thereby, each complementary section is set (step S43).

Then, the complementary section extraction unit 41 updates the data index s by adding 1 to the data index s (step S44).
Here, the complementary section extraction means 41 compares the updated data index s with the predetermined number of actual data S (step S45), and the stage where the data index s becomes S or more (No in step S45). ) To finish the operation.
On the other hand, when the data index s is less than S (Yes in step S45), the retroactive amount i is updated by adding 1 to the retroactive amount i (step S46).

Here, the complementary section extraction means 41 compares the updated retroactive amount i with the maximum retroactive amount _Nlim (step S47), and when the retroactive amount i is equal to or less than the maximum retroactive amount _Nlim (Yes in step S47). Returns to step S42 to continue the operation.
On the other hand, when the retroactive amount i exceeds the maximum retroactive amount _Nlim (No in step S47), the operation of extracting the complementary section is ended.

With the above operation, the supplementary interval extracting means 41 can set the intervals U _{0 to} U _S shown in the above equation (7). The complementary section extracted in this way and the actual data value D _R [s] set in step S43 are used when determining the interpolation function in step S6 of FIG.

[Specific example of data completion operation]
Next, a specific example of the interpolation operation in the time-series data complementing apparatus 1 will be described with reference to FIGS. 7 to 15 (see FIG. 1 as appropriate). 7 to 15 show the contents of the storage means that are updated each time time-series data is input, and the extracted contents of the complementary section at that time.
Here, the array size N of the data area Da and the attribute area Aa (see FIG. 2) in the storage means 10 is “10”, the maximum retroactive amount N _lim is “9”, and the current time in the data input means 20 Is set to “0”, and the retroactive amount d from the current time in the data output means 30 is set to “2”.
Here, the interpolation function P (u) is a linear function or zero-order hold. The order and coefficient of this interpolation function are determined according to the following rules (Rule i) to (Rule vi).

(Rule i) N _after (s) = 0 and N _before (s) = 0 ... No complement (Rule ii) N _after (s) = 1 and N _before (s) = 0 ... D _R [ Complement by zero-order hold of s-1] (Rule iii) When N _after (s) = 0 and N _before (s) = 1 ... D _R Complement by zero-order hold of [s] (Rule iv) N _after ( When s) ≧ 1 and N _before (s) ≧ 1, it is complemented by a straight line (linear function) passing through D _R [s−1] and D _R [s] (rule v) N _after (s) ≧ 2 and When N _before (s) = 0: complemented by a straight line (linear function) passing through D _R [s-1] and D _R [s-2] (rule vi) N _after (s) = 0 and N _before ( s) In case of ≧ 2: complemented by a straight line (linear function) passing through D _R [s] and D _R [s + 1]

Here, N _after (s) is the number of actual data input after a certain section (see the above equation (8)), and N _before (s) is the number of actual data input before a certain section. (Refer to the formula (9)). D _R [s] and the like are actual data values of the sth (retroactive amount T _R (s)) from the current time.
Here, it is assumed that the input time series data is {5, 7, NaN, 13, NaN, NaN, 16, NaN, NaN} (NaN indicates that data is missing).

As shown in <data input time> in FIG. 7A, when the data _Din = 5 is input at the current time t = 0, the data input means 20 causes the write address w (here, the address Ad "00"). ")" Is written in the data area Da, and the attribute value "1" indicating the actual data is written in the attribute area Aa. In the figure, ● indicates that data has been written.
Then, as shown in FIG. 7 (b), the data complementing means 40 uses the above equation (7) to _obtain a complementing section in which the section U ₀ = φ (empty set) and the section U ₁ = (0, N _lim +1). Is extracted, and the interpolation is performed on the section U ₁ .
At this time, N _after (1) = 1 from the above equation (8), N _before (1) = 0 from the above equation (9), and in the case of (rule ii), the interpolation function P (u) Is zero-order hold P (u) = D _R [00] = 5.

Therefore, as shown in <Complementary processing result> in FIG. 7A, the data complementing means 40 holds zero-order hold of the value of D [00] in D [01] to D [09] of the data area Da. That is, the copy value (“5”) is written. In the figure, ■ indicates that data has been updated by the complement processing. At this time, the data complementing means 40 writes an attribute value “2” indicating that the data value is interpolation data in A [01] to A [09] of the attribute area Aa.
Since the data output means 30 has the retroactive amount d = 2, the data output means 30 stores the data area Da at the read address r (here, address Ad “08”) at the current time t−2 (t _out = −2). The value “5” is read and output.

Next, as shown in <data input time> in FIG. 8A, when data D _in = 7 is input at the current time t = 1, the data input means 20 reads the write address w (in this case, the address "7" is written in the data area Da of "Ad" 01 "), and the attribute value" 1 "indicating the actual data is written in the attribute area Aa.
Then, as shown in FIG. 8B, the data complementing means 40 uses the equation (7) to obtain the section U ₀ = U ₁ = φ (empty set) and the section U ₂ = (1, N _lim +1). Is extracted, and the interpolation is performed on the section U ₂ .
At this time, N _after (2) = 2 from the above equation (8), N _before (2) = 0 from the above equation (9), and in the case of (rule v), the interpolation function P (u) Is a linear function P (u) = 7-2u.

Therefore, the data complementing means 40 writes the data values in D [02] to D [09] of the data area Da as shown in <Complementary processing result> in FIG. At this time, the data complementing means 40 writes the attribute value “2” indicating that the data value is interpolation data in A [02] to A [09] of the attribute area Aa.
Since the data output means 30 has the retroactive amount d = 2, the data output means 30 in the data area Da at the read address r (here, address Ad “09”) at the current time t−2 (t _out = −1). The value “3” is read and output.

Next, as shown in <data entry> in FIG. 9 (a), at the current time t = 2, the data D _in = NaN, that is, when data is lost, the data input unit 20, a write address w (where Then, an arbitrary value is written in the data area Da of the address Ad “02”), and an attribute value “0” indicating missing data is written in the attribute area Aa. It is not always necessary to write a data value in the data area Da.
Then, as shown in FIG. 9B, the data complementing means 40 uses the equation (7) to obtain the section U ₀ = (− 1, 1), the section U ₁ = φ, and the section U ₂ = (2, N _lim + 1) is extracted, and the interpolation is performed on the sections U ₀ and U ₂ .
At this time, in section U ₀ , N _after (2) = 2 from the equation (8), N _before (2) = 0 from the equation (9), and the above (rule vi) is satisfied, The interpolation function P (u) is linear function P (u) = 9-2u. In the section U ₂ , N _after (1) = 2 from the above equation (8), N _before (2) = 0 from the above equation (9), which matches the above (rule v), the interpolation is performed. The function P (u) is a linear function P (u) = 9-2u.

Therefore, the data complementing means 40 writes the data value in D [02] to D [09] of the data area Da as shown in <Complementary processing result> in FIG. At this time, the data complementing means 40 writes the attribute value “2” indicating that the data value is interpolation data in A [02] to A [09] of the attribute area Aa.
Since the data output means 30 has the retroactive amount d = 2, the value of the data area Da at the read address r (here, address Ad “00”) at the current time t−2 (t _out = 0). Read and output “5”.

Further, as shown in <data input time> in FIG. 10A, when data D _in = 13 is input at the current time t = 3, the data input means 20 causes the write address w (here, the address Ad). “13” is written in the data area Da of “03” and the attribute value “1” indicating the actual data is written in the attribute area Aa.

Then, as shown in FIG. 10B, the data complementing means 40 calculates the section U ₀ = φ (empty set), the section U ₁ = (0, 2), and the section U ₂ = φ from the equation (7). Then, a supplementary section in which the section U ₃ = (3, N _lim +1) is extracted, and the supplement is executed on the sections U ₁ and U ₃ .
In this section U ₁ , N _after (1) = 1 from the equation (8), N _before (1) = 2 from the equation (9), and the above (rule iv), the interpolation function is satisfied. P (u) is a linear function P (u) = 13-3u.
In the section U ₃ , N _after (3) = 3 from the above equation (8), N _before (3) = 0 from the above equation (9), and the above (rule v) is met. The function P (u) is a linear function P (u) = 11-2u.

Therefore, the data complementing means 40 writes the data value in D [02], D [04] to D [09] of the data area Da as shown in <Complementary processing result> in FIG. At this time, the data complementing means 40 writes the attribute value “2” indicating that the data value is interpolation data in A [02], A [04] to A [09] of the attribute area Aa.
Since the data output means 30 has the retroactive amount d = 2, the value of the data area Da at the read address r (here, address Ad “01”) at the current time t−2 (t _out = 1). Read and output “7”.

In the following, in FIGS. 11 to 15, similarly to FIGS. 7 to 10, an interpolation function is determined for each complement section, and the missing data is complemented sequentially based on the interpolation function.
As a result, {5, 3, 5, 7, 10, 13, 14, 15, 16 for the input time-series data {5, 7, NaN, 13, NaN, NaN, 16, NaN, NaN}. } Time-series data is generated. Here, since the output data is output with a delay of 2 unit times from the input data (retroactive amount e = 0, retroactive amount d = 2), the first seven of the input time-series data, that is, {5, 7, NaN, 13, NaN, NaN, 16} are complemented with data delayed by 2 unit times in the output data, that is, {5,7,10,13,14,15,16} and output. In this way, the actual data is held as it is among the input time-series data, and a data string that is appropriately complemented only for the missing data (NaN) is generated.

It is the block diagram which showed the structure of the time series data complementation apparatus which concerns on this invention. It is a block diagram which shows the arrangement structure of the data memorize | stored in a memory | storage means. It is explanatory drawing for demonstrating the relationship of writing and reading of data in the arrangement | sequence memorize | stored in a memory | storage means. It is explanatory drawing for demonstrating the concept of a supplementary area, Comprising: (a) shows the time series data with the input missing, (b) shows the example which extracted the supplementary area with respect to the time series data. Yes. It is a flowchart which shows the whole operation | movement of the time series data complementation apparatus which concerns on this invention. It is a flowchart which shows the operation | movement of the complementary area extraction performed by the complementary area extraction means of the time series data complementation apparatus which concerns on this invention. It is explanatory drawing for demonstrating the content of a complementation process, Comprising: (a) has shown the content of the memory | storage means in the time of t = 0, (b) has shown the extraction content of the complementary area at that time. It is explanatory drawing for demonstrating the content of a complementation process, Comprising: (a) has shown the content of the memory | storage means in the time of t = 1, (b) has shown the extraction content of the supplementary area at that time. It is explanatory drawing for demonstrating the content of a complementation process, Comprising: (a) has shown the content of the memory | storage means in the time of t = 2, (b) has shown the extraction content of the complementary area at that time. It is explanatory drawing for demonstrating the content of a complementation process, Comprising: (a) has shown the content of the memory | storage means in the time of t = 3, (b) has shown the extraction content of the complementary area at that time. It is explanatory drawing for demonstrating the content of a complementation process, Comprising: (a) shows the content of the memory | storage means in the time of t = 4, (b) has shown the extraction content of the supplementary area at that time. It is explanatory drawing for demonstrating the content of a complementation process, Comprising: (a) has shown the content of the memory | storage means in the time of t = 5, (b) has shown the extraction content of the supplementary area at that time. It is explanatory drawing for demonstrating the content of a complementation process, Comprising: (a) has shown the content of the memory | storage means in the time of t = 6, (b) has shown the extraction content of the supplementary area at that time. It is explanatory drawing for demonstrating the content of a complementation process, Comprising: (a) has shown the content of the memory | storage means in the time of t = 7, (b) has shown the extraction content of the complementary area at that time. It is explanatory drawing for demonstrating the content of a complementation process, Comprising: (a) has shown the content of the memory | storage means in the time of t = 8, (b) has shown the extraction content of the complementary area at that time.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Time series data complementing apparatus 10 Memory | storage means 20 Data input means 30 Data output means 40 Data complementing means 41 Complementary area extraction means 42 Complementary means 42a Actual data counting means 42b Interpolation function determining means 42c Complementary data generating means 43 Data updating means

Claims (6)

A time-series data complementing device that inputs time-series data with missing data and supplements the missing data based on actual data that is the time-series data,
Storage means for storing the time-series data;
Data input means for inputting the time series data and writing the time series data in the time series in the storage means;
In the time-series data stored in the storage unit, the time-series data in a predetermined time interval corresponds to the number of the actual data input before or after the missing data. A data complementing unit that generates complemented data that complements the missing data by an interpolation function, and stores the data in the storage unit;
Data output means for reading out the complementary data supplemented by the data complementing means or the actual data in time series from the storage means;
A time-series data complementing device comprising: The data complementing means is:
Based on the time-series data stored in the storage means, a complementary interval extracting means for extracting the complementary interval lacking the data;
Real data counting means for measuring the number of the actual data in a predetermined time interval at least either before or after the time series of the complementary interval extracted by the complementary interval extraction means;
Interpolation function determining means for determining the interpolation function based on the number of actual data measured by the actual data counting means and the value of the actual data;
Based on the interpolation function determined by the interpolation function determining means, complementary data generating means for generating complementary data that complements the missing data in the complementary section;
Data updating means for updating the missing data in the storage means by means of the complementary data generated by the complementary data generating means;
The time-series data complementing device according to claim 1, comprising:   2. The data input means, when writing the time series data in time series in the storage means, writes the time series data in a region shifted in the past by a predetermined delay time. Or the time-sequential data complementation apparatus of Claim 2.   2. The data output means, when reading the time series data in time series from the storage means, reads the time series data from an area shifted in the past by a predetermined delay time. The time series data complementing device according to any one of claims 3 to 4. A time series data complementing method that inputs time series data with missing data and supplements the missing data based on the actual data that is the time series data,
A data input step of inputting the time series data and writing the time series data in a time series in a storage means;
In the time-series data stored in the storage unit, the time-series data in a predetermined time interval corresponds to the number of the actual data input before or after the missing data. A data complementing step of generating complementing data that complements the missing data by an interpolation function, and storing it in the storage means;
A data output step of reading out and outputting the complemented data or the actual data complemented in this data complementing step in time series from the storage means;
A time series data complementing method characterized by comprising: To input time series data with missing data, and to supplement the missing data based on the actual data that is the time series data,
Data input means for inputting the time series data and writing the time series data to the storage means in time series,
Based on the time-series data stored in the storage means, a complementary interval extracting means for extracting the complementary interval lacking the data;
Real data counting means for measuring the number of the actual data in a predetermined time interval at least either before or after the time series of the complementary interval extracted by the complementary interval extraction means;
Interpolation function determining means for determining the interpolation function based on the number of actual data measured by the actual data counting means and the value of the actual data;
Based on the interpolation function determined by the interpolation function determining means, complementary data generating means for generating complementary data that complements the missing data in the complementary section;
Data updating means for updating the missing data in the storage means by means of the complementary data generated by the complementary data generating means;
Data output means for reading the complementary data updated by the data update means or the actual data in time series from the storage means, and outputting the data,
A time series data complementing program characterized by functioning as

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