JP6604212B2 - Data processing apparatus, data processing method, and data processing program - Google Patents

Description

  The present invention relates to a data processing device, a data processing method, and a data processing program.

  A technique is used in which similarity between two time series data is calculated by comparing two time series data among a plurality of time series data. One of the methods for calculating the similarity is an operation using Kendall's rank correlation coefficient.

  As a related technique, a technique called high-speed all pair similarity search by a composite sort method has been proposed. In this technique, the magnitude relationship of values is stored as a character string for each data period to be compared (for example, see Non-Patent Document 1).

  In addition, the portable device measures the reception strength of the measurement unit of the authentication request signal, and whether the authentication request signal is a legitimate signal based on whether the change in the magnitude relationship of the reception strength matches a predetermined pattern. Has been proposed (see, for example, Patent Document 1).

  Further, a technique has been proposed in which the magnitude relationship between the terminal voltage and the predetermined voltage is sampled in time series, and the energization control is performed based on the sampled magnitude relationship and regular changes (see, for example, Patent Document 2). ).

Koji Tsuda, “Fast All Pair Similarity Search Using Compound Sort Method”, ERATO 湊 Discrete Structure Processing Project, 2010 ERATO 湊 Discrete Structure Processing Project Proceedings. P.490-495.

JP 2005-269719 A JP 2014-139552 A

  For example, in the method of storing the value magnitude relationship as a character string for each data period of the time-series data to be compared, the amount of value magnitude information increases. For this reason, the amount of information used when calculating the similarity of time-series data increases, and the calculation time increases.

  As one aspect, an object of the present invention is to shorten the calculation time when comparing time series data.

In one embodiment, the data processing device, for each of the two time series data to be compared, a detector for detecting a change point increase or time trend of decrease the value changes over time, when the two Within a predetermined period including a plurality of the same period widths set individually for each of the series data, the two time-series data are set to the first time within the predetermined period for each of the plurality of the same period widths. A counter that counts the number of matches in which the change in tendency at the corresponding time in the same order coincides from the detection time of the change point with respect to the two time-series data when sequentially compared in the same order from A calculation unit that calculates a similarity between the two time-series data based on the number of matches .

  According to one aspect, the calculation time for comparing time series data can be shortened.

It is a figure which shows an example of the calculation using Kendall's rank correlation coefficient. It is a functional block diagram which shows an example of a data processor. It is a figure which shows an example of the hardware constitutions of a data processor. It is a figure which shows an example of the method of calculation of similarity. It is FIG. (1) explaining an example of a change point detection. It is FIG. (2) explaining an example of a change point detection. It is FIG. (1) explaining an example of the calculation of the similarity degree when not shifting a window. It is FIG. (2) explaining an example of the calculation of the similarity degree when not shifting a window. It is FIG. (1) which shows an example of the calculation of the similarity in the case of shifting both windows. It is FIG. (2) which shows an example of the calculation of the similarity in the case of shifting both windows. It is FIG. (3) which shows an example of the calculation of similarity in the case of shifting both windows. It is FIG. (4) which shows an example of the calculation of the similarity in the case of shifting both windows. It is FIG. (5) which shows an example of the calculation of the similarity in the case of shifting both windows. FIG. 10 is a diagram (part 1) illustrating an example of similarity calculation when one window is shifted; It is FIG. (2) which shows an example of the calculation of the similarity in the case of shifting one window. FIG. 11 is a diagram (part 3) illustrating an example of similarity calculation when one window is shifted; It is FIG. (4) which shows an example of the calculation of the similarity in the case of shifting one window. It is FIG. (5) which shows an example of the calculation of the similarity in the case of shifting one window. It is FIG. (6) which shows an example of the calculation of the similarity in the case of shifting one window. It is FIG. (7) which shows an example of the calculation of the similarity in the case of shifting one window. It is a figure which shows three specific examples of the calculation of the similarity of time series data. It is FIG. (The 1) explaining the specific example 1. FIG. It is FIG. (2) explaining the specific example 1. FIG. FIG. 6 is a third diagram illustrating a first specific example. FIG. 4 is a diagram (part 4) for explaining a specific example 1; FIG. 5 is a fifth diagram illustrating a first specific example; It is FIG. (6) explaining the specific example 1. FIG. FIG. 7 is a diagram (part 7) for explaining a specific example 1; It is FIG. (The 8) explaining the specific example 1. FIG. It is FIG. (9) explaining the specific example 1. FIG. 10 is a diagram (No. 10) for explaining a specific example 1; It is FIG. (11) explaining the specific example 1. It is FIG. (12) explaining the specific example 1. FIG. It is FIG. (13) explaining the specific example 1. It is FIG. (14) explaining the specific example 1. It is FIG. (15) explaining the specific example 1. FIG. It is FIG. (16) explaining the specific example 1. FIG. It is FIG. (17) explaining the specific example 1. It is FIG. (18) explaining the specific example 1. It is FIG. (19) explaining the example 1. It is FIG. (The 21) explaining the specific example 1. It is FIG. (22) explaining the specific example 1. It is FIG. (23) explaining the specific example 1. It is FIG. (The 24) explaining the specific example 1. FIG. It is FIG. (25) explaining the specific example 1. It is FIG. (26) explaining the specific example 1. It is FIG. (27) explaining the specific example 1. FIG. It is FIG. (28) explaining the specific example 1. It is FIG. (29) explaining the specific example 1. It is FIG. (30) explaining the specific example 1. It is FIG. (The 31) explaining the specific example 1. FIG. It is FIG. (1) explaining the specific example 2. FIG. It is FIG. (2) explaining the specific example 2. It is FIG. (3) explaining the specific example 2. It is FIG. (4) explaining the specific example 2. FIG. 6 is a diagram (part 5) illustrating a specific example 2; It is FIG. (6) explaining the specific example 2. It is FIG. (The 7) explaining the specific example 2. FIG. It is FIG. (8) explaining the specific example 2. FIG. It is FIG. (9) explaining the specific example 2. It is FIG. (10) explaining the specific example 2. It is FIG. (11) explaining the specific example 2. It is FIG. (12) explaining the specific example 2. FIG. It is FIG. (13) explaining the specific example 2. It is FIG. (14) explaining the specific example 2. It is FIG. (15) explaining the specific example 2. It is FIG. (1) explaining the specific example 3. It is FIG. (2) explaining the specific example 3. FIG. 10 is a third diagram illustrating a third specific example; FIG. 6 is a diagram (part 4) illustrating a specific example 3; FIG. 10 is a diagram (part 5) illustrating a specific example 3; It is FIG. (6) explaining the example 3. It is FIG. (7) explaining the specific example 3. It is FIG. (The 8) explaining the specific example 3. FIG. It is FIG. (9) explaining the specific example 3. It is FIG. (10) explaining the specific example 3. It is FIG. (11) explaining the specific example 3. It is FIG. (12) explaining the specific example 3. It is FIG. (13) explaining the specific example 3. It is FIG. (14) explaining the specific example 3. It is FIG. (15) explaining the specific example 3. It is FIG. (16) explaining the specific example 3. It is FIG. (17) explaining the example 3. It is FIG. (18) explaining the specific example 3. It is an example (the 1) of the number of matches using other values. It is an example (the 2) of the number of matches using other values. It is an example (the 3) of the number of matches using other values. It is an example (the 4) of the number of coincidence using other values. It is an example (the 5) of the number of matches using other values. It is an example (the 6) of the number of matches using other values. It is a flowchart (the 1) which shows an example of the flow of a process of embodiment. It is a flowchart (the 2) which shows an example of the flow of a process of embodiment. It is a flowchart (the 3) which shows an example of the flow of a process of embodiment. It is a flowchart (the 4) which shows an example of the flow of a process of embodiment. It is a flowchart (the 5) which shows an example of the flow of a process of embodiment. It is a figure which shows an example of three types of time series data.

  Hereinafter, embodiments will be described with reference to the drawings. In the embodiment, the similarity between time series data is calculated using Kendall's rank correlation coefficient. The time series data is data representing values at each time. In the example of FIG. 1, it is assumed that time series data to be compared is data 1 and data 2.

  In the case of the example of FIG. 1, it is assumed that the data size of data 1 and data 2 is “4”. Hereinafter, the data size may be referred to as the number of items. The data size (number of items) is the number of values at each time of the time series data.

  When the similarity calculation is performed using Kendall's rank correlation coefficient, the above similarity calculation is performed based on the number of coincidence of the magnitude relationships between the values of the two time-series data to be compared. Is called.

  For example, the value of data 1 at time (noted as an item in FIG. 1) “T3” is “7.2”, which is larger than the value at time “T4”. The value of data 2 at time “T3” is “2.2”, which is larger than the value at time “T4”. In this case, the magnitude relationship between the time “T3” and the time “T4” between the data 1 and the data 2 is the same.

The similarity t using the Kendall rank correlation coefficient is expressed by the following equation (A).
t = (4 * P / n * (n-1))-1 ... Formula (A)

  Hereinafter, the similarity may be referred to as a correlation value. In the formula (A), P is the number (the number of matches) in which the magnitude relationship between data 1 and data 2 matches. n is the number of items. In the example of FIG. 1, the number of items n is “4”.

  In the case of the example of FIG. 1, the number of data 1 and data 2 having the same magnitude relationship is “4”, so “P = 4”. Therefore, when the item number n and the coincidence number P are applied to the equation (A), the similarity t is “t = (4 × 4 × / (4 × (4-1))) = 0.33”.

<Example of data processing device>
FIG. 2 shows an example of the data processing apparatus 1 of the embodiment. The data processing device 1 includes a storage unit 11, a detection unit 12, a counting unit 13, a calculation unit 14, and a difference processing unit 15. The data processing device 1 is an example of a computer.

  The storage unit 11 stores various types of information. For example, the storage unit 11 stores a plurality of time series data. The plurality of time-series data may be, for example, data measured by different sensors, or data indicating changes in sales of different products over time.

  The detection unit 12 detects a change point at which the magnitude relationship between the times changes for each time difference in the two time series data to be compared among the plurality of time series data stored in the storage unit 11. Based on the change point detected by the detection unit 12, the counting unit 13 counts the number of coincidence of two time-series data as the number of matches.

  The calculating unit 14 calculates the similarity t between the two time-series data by fitting the coincidence number P and the item number n counted by the counting unit 13 to the above-described equation (A). The difference processing unit 15 performs a process of shifting the comparison target period of the two time-series data, and various processes when the period is shifted.

<Example of hardware configuration of data processing apparatus>
Next, an example of the hardware configuration of the data processing apparatus 1 will be described with reference to the example of FIG. As shown in the example of FIG. 3, a processor 111, a random access memory (RAM) 112, a read only memory (ROM) 113, an auxiliary storage device 114, a medium connection unit 115, and a communication interface 116 are connected to the bus 100. Has been.

  The processor 111 is an arbitrary processing circuit. The processor 111 executes a program expanded in the RAM 112. As a program to be executed, a data processing program for performing the processing of the embodiment may be applied. The ROM 113 is a non-volatile storage device that stores programs developed in the RAM 112.

  The auxiliary storage device 114 is a storage device that stores various types of information. For example, a hard disk drive or a semiconductor memory may be applied to the auxiliary storage device 114. The medium connection unit 115 is provided so as to be connectable to the portable recording medium 119.

  As the portable recording medium 119, a portable memory or an optical disc (for example, Compact Disc (CD), Digital Versatile Disc (DVD), etc.) may be applied. A program for performing the processing of the embodiment may be recorded on the portable recording medium 119.

  In the data processing device 1, the storage unit 11 may be realized by the RAM 112, the auxiliary storage device 114, and the like. The detection unit 12, the counting unit 13, the calculation unit 14, and the difference processing unit 15 may be realized by the processor 111 executing a given data processing program.

  The RAM 112, the ROM 113, the auxiliary storage device 114, and the portable recording medium 119 are all examples of a tangible storage medium that can be read by a computer. These tangible storage media are not temporary media such as signal carriers.

<Example of similarity calculation method>
In the embodiment, the calculation unit 14 calculates the similarity between two time-series data using a plurality of types of methods. FIG. 4 shows an example of the following three types of similarity calculation methods (1) to (3).

  (1) shows an example of calculating similarity of four time-series data in the same period. In the example of FIG. 4, it is shown as “comparison of four data”. In this case, the calculation unit 14 calculates the similarity of each pair of two time-series data among the four time-series data. The number of time series data to be compared is not limited to four.

(2) shows an example in which the similarity between two time series data is calculated while the comparison target periods are shifted for both of the two time series data.
An example of performing

  (3) shows an example in which one of the two time-series data is fixed and the similarity between the two time-series data is calculated while one of the comparison target periods is shifted.

  In (1) to (3), all the times of the two time-series data may be targets for counting the number of matches, or some periods of the two time-series data are counted for the number of matches. It may be a target.

  Hereinafter, the period for which the number of matches is counted is referred to as a window. In (2), the difference processing unit 15 obtains the amount of change in the number of matches each time the windows of the two time series data are shifted once.

  When the difference processing unit 15 shifts the window, the window is shifted (moved) to a time one time after the time-series data. The window is set to start at the first time in the time zone to be compared, and is shifted to the next time. The same applies to (3).

<Example of change point detection>
FIG. 5 shows an example of change point detection of time series data. In the example of FIG. 5, each value from time “1” to “10” is shown as time-series data of data 1. The time series data is stored in the storage unit 11.

  For each time difference, the detection unit 12 compares the magnitude relations of the time values before and after each time of the time-series data, and detects a change point (change time) at which the magnitude relation changes. In the embodiment, when the value of the previous time is small as seen from the value of the next time according to the time difference, the magnitude relationship is “−”.

  In the embodiment, when the value of the previous time is large as viewed from the value of the next time according to the time difference, the magnitude relationship is “+”. For example, in the example of FIG. 5, when the time difference is “2”, the value of time “3” is larger between the value of time “1” and the value of time “3”. Therefore, the magnitude relationship between the time “1” and the time difference “2” is “−”.

  On the other hand, when the time difference is “2”, the value of time “5” is small between the value of time “3” and the value of time “5”. Therefore, the magnitude relationship of the time “3” in the time difference “2” is “+”. Therefore, in the example of FIG. 5, when the time difference is “2”, the magnitude relationship changes at time “3”.

  The detection unit 12 detects a change point where the magnitude relationship between the previous and next times changes for each time difference, and stores data indicating the detected change point in the storage unit 11 as change point data. The detection unit 12 stores, in the storage unit 11, change point data in a format in which information indicating the detected change point is expressed by a time and a magnitude relationship.

  For example, in the example of FIG. 5, the detection unit 12 detects that the magnitude relationship changes to “+” at the time difference “2” and the time “3”. The detection unit 12 stores the change point data corresponding to the time difference “2” in the storage unit 11 in the format “3+”.

  In the example of FIG. 5, a two-dimensional matrix (sometimes referred to as a two-dimensional table) is shown. In the matrix after FIG. 5, the values of the time-series data at each time are developed in the X direction and the Y direction. The elements of the matrix represent the magnitude relationship of each time of the time series data at each time difference.

  In the matrix, the solid line indicates that the magnitude relationship is “+”, and the dotted line indicates that the magnitude relationship is “−”.

  The matrix after FIG. 5 is an image visualizing the magnitude relationship. In the matrix, the magnitude relationship at each time for each time difference is described. Accordingly, the amount of magnitude-related information increases, and the processing time when the counting unit 13 counts the number of coincidence of magnitude relations becomes long.

  Therefore, in the embodiment, the counting unit 13 counts the number of coincidence of magnitude relations without using the matrix illustrated in FIG. In the embodiment, the counting unit 13 counts the number of matches in magnitude relation based on the change point data.

  In the matrix from FIG. 5 onward, each element in the diagonal direction indicates a magnitude relationship for one time difference. The time difference increases each time the starting point of each element in the oblique direction is shifted in the X direction. In the case of the example of FIG. 5, each element in the oblique direction starting from the time “3” in the X direction and the time “1” in the Y direction represents the magnitude relationship at the time difference “2” (the chain line in FIG. 5).

  Referring to the example of the matrix in FIG. 5, when the time difference is “2”, the magnitude relationship changes at times “1”, “3”, and “7” in the Y direction. The detection unit 12 searches the time series data to detect change point data at the time difference “2”.

  FIG. 6 shows an example of change point detection when the time difference is “2”. In the example of FIG. 6, for the sake of explanation, an example of detection of change points using a matrix is shown, but the detection unit 12 detects change points without using a matrix.

  The first change point of the time difference “2” (initial value in the example of FIG. 6) is “1”. The detection unit 12 determines whether or not a section (block) between the first change point and the next change point is separated. In the example of FIG. 6, this section is times “3” to “5” in the X direction and times “1” to “3” in the Y direction.

  Whether or not the sections are separated is determined by whether or not the values overlap between the value range in the X direction and the value range in the Y direction of the section. The range of the value in the X direction in this section is “7.5” to “4.5”, and the value in the Y direction is “2.1” to “7.5”.

  In this case, the values “4.5” to “7.5” overlap. Therefore, the detection unit 12 determines that the above-described section is a “non-separated” section and detects a change point. On the other hand, the detection unit 12 does not detect change points in the “separated” section, the same monotone decreasing section, and the same monotone increasing section.

  The monotonically increasing interval is an interval in which the time series data value increases without decreasing. The monotonically decreasing interval is an interval in which the time series data value decreases without increasing. This is because there are no change points in the same monotonically increasing section and the same monotonically decreasing section.

  For a section that is not separated, when the section size is large, the detection unit 12 may detect the change point by dividing the section into a plurality of sections.

<Example of similarity calculation when the window is not shifted>
An example of the number of matches in the magnitude relationship between data 1 and data 2 will be described. In the example of FIG. 7, two time series data of data 1 and data 2 are stored in the storage unit 11. The counting unit 13 compares the two time-series data and counts the number of coincidence in magnitude.

  In the case of the example in FIG. 7, the comparison target period (window) of data 1 is from time “2” to “6”, and the window of data 2 is from time “4” to “8”. Therefore, the window range is “5”. Hereinafter, the window range may be referred to as a period width. The window range is an example of a period for counting the number of matches.

  FIG. 8 shows an example of the count of the number of matches of the two data shown in the example of FIG. The counting unit 13 counts the number of coincidence in magnitude relation for each period width (window) of data 1 and data 2.

  Since the comparison target is the magnitude relationship between the values of the time series data, the counting unit 13 compares the magnitude relationships within a range obtained by subtracting “1” from the period width. Data 1 and data 2 have different leading times.

  The counting unit 13 counts the number of matching in order from the top time. The counting unit 13 uses an index to align the top times of data 1 and data 2. The storage unit 11 stores change point data for each time difference between the data 1 and the data 2.

  The counter 13 subtracts a value obtained by subtracting “1” from the leading time from each value of the change point data of the data 1 and the data 2 in order to align the indexes. For example, the counting unit 13 subtracts “2-1 = 1” from each value of the change point data of the data 1. Further, the counting unit 13 subtracts “4-1 = 3” from each value of the change point data of the data 2.

  Thereby, the start points of data 1 and data 2 are aligned by the index. The counting unit 13 counts the number of matches between the data 1 and the data 2 in the window range “1” to “3”.

  The magnitude relationship in index 1 is “-” for both data 1 and data 2. Accordingly, since the magnitude relationship between the two matches, the counting unit 13 adds (increments) the number of matches in the magnitude relationship. The initial value of the number of matches in the magnitude relationship is zero.

  As for the magnitude relationship in index 2, data 1 changes to “+” and data 2 is “−”. Regarding the magnitude relationship in the index 3, the data 1 is “+” and the data 2 is “−”. In these cases, since the magnitude relationship between the two does not match, the number of matches in the magnitude relationship does not change.

  Accordingly, the counting unit 13 counts the number of coincidence of magnitude relations within the window range as “1”. The counting unit 13 counts the number of coincidence between the data 1 and the data 2 for the time differences “1”, “3”, and “4” in the same manner as the time difference “2”.

  In the example of FIG. 8, the total number of matches is “2”. The total “2” of the number of matches is the number of matches P in the above-described formula (A). The computing unit 14 fits the number of items n (n = 5) and the number of matches P (P = 8) in the window range to the above-described equation (A), and obtains the similarity t = “− 0.60”.

<Example of similarity calculation when shifting both windows>
Next, an example of similarity calculation when both the data 1 and data 2 windows are shifted will be described. As described above, the counting unit 13 counts the number of matches in the magnitude relationship between the data 1 and the data 2 in the window shown in the example of FIG. In this case, the coincidence number P is “2”.

  The difference processing unit 15 shifts each window of data 1 and data 2 backward by one in the time axis direction. The counting unit 13 counts the number of coincidence of the magnitude relation between the data 1 and the data 2 based on whether or not the changing point has entered the window range and whether or not the changing point has come out from the window range. To do.

  In FIG. 9 and subsequent figures, the window range surrounded by a solid line indicates a range before the window is shifted, and the window range surrounded by a dotted line indicates a range after the window is shifted.

  In the case of the example in FIG. 9, the difference processing unit 15 shifts the window, so that the number of matches increases by two and decreases by two. Therefore, the amount of change in the number of matches is “0 = 2-2”. Since the coincidence number P before the window is shifted is “2”, the counting unit 13 counts the coincidence number P as “2 = 2 + 0”.

  The example of FIG. 10 shows the case where the position of the window changes in the matrix, the case where the change point exits the window, and the case where the window enters the window. As described above, the matrix is an image of the magnitude relationship of time series data.

  In FIG. 10 and subsequent figures, the reference window indicates a window before being shifted by the difference processing unit 15. The updated window indicates the window after being shifted by the difference processing unit 15.

  In the example of FIG. 11, the magnitude relations of the front ends (time “6” in the X direction and times “2” to “6” in the Y direction) in the reference window in the data 1 are all “+”. All the magnitude relations of the front end (time “8” in the X direction and times “4” to “8” in the Y direction) in the reference window in the data 2 are “−”.

  Therefore, the number of matches in the magnitude relationship at the tip in the window before the window is shifted is zero.

  The magnitude relations of the rear end outside the reference window in data 1 (time “1” in the Y direction and times “2” to “6” in the X direction) are all “−”. The magnitude relations of the rear end outside the reference window in data 1 (time “3” in the Y direction and times “4” to “8” in the X direction) are all “−”.

  Accordingly, the number of coincidence of the magnitude relationship at the rear end outside the window before the window is shifted is “4”. The amount of change in the number of matches is “−4 = 0−4”.

  If the changing point does not enter or exit the window when the window is shifted, the amount of change in the number of matches is constant. On the other hand, when the change point enters and exits the window when the window is shifted, the amount of change in the number of matches changes.

  In the example of FIG. 11, the number of matches after the window is shifted (after update) is “2”. With reference to the example of FIG. 12, an example in which a change point is included in the window when the window is shifted will be described.

  The difference processing unit 15 shifts the windows for data 1 and data 2. The difference processing unit 15 refers to the change point data and determines whether or not the change point enters and exits the window when the window is shifted.

  The difference processing unit 15 reverses the magnitude relationship between the change points when the change point specified by the change point data enters and exits the window when the windows of the time series data of the data 1 and the data 2 are shifted. .

  In the case of the example in FIG. 12, before the window is shifted, the size relationship between the front ends of the windows with the time differences “1” and “2” is “x”. As the window is shifted, a change point is entered at the front end in the window of the time difference “1” and “2”. Therefore, the difference processing unit 15 inverts the magnitude relationship between the change points at the time differences “1” and “2”.

  Further, before the window was shifted, the size relationship between the rear end outside the window of the time difference “3” and “4” was “◯”. By shifting the window, a change point appears from the rear end outside the window of the time difference “3” and “4”. Accordingly, the difference processing unit 15 inverts the magnitude relationship between the change points at the time differences “3” and “4”.

  As a result, the number of matches at the front end in the window between data 1 and data 2 is “2”, and the number of matches at the rear end outside the window is “2”. Therefore, the difference processing unit 15 obtains the amount of change “0 = 2-2” in the number of matches. Since the number of matches before the window is shifted is “2”, the difference processing unit 15 obtains the number of matches “2 = 2 + 0”.

  Next, an example of a management table indicating the positional relationship of change points with respect to the window will be described with reference to the example of FIG. The detection unit 12 detects a change point at which the magnitude relationship between the data 1 and the data 2 changes. In the embodiment, the management table is stored in the storage unit 11.

  Further, as described above, when the windows of both data 1 and data 2 are shifted, the number of coincidence of magnitude relations within the range of the window is obtained based on the change point entering the window and the change point exiting from the window.

  Then, based on the obtained coincidence number P, the calculation unit 14 performs a calculation based on the above-described equation (A), whereby the similarity between the two time-series data is calculated each time the window is shifted.

  The detection unit 12 detects a change point of the magnitude relationship. The counting unit 13 manages the positional relationship between the window and the change point. In the embodiment, the difference processing unit 15 manages the positional relationship between the window and the change point using the management table illustrated in the example of FIG.

  For example, in data 2, before the window shifts (before update), the change points No. 9 and No. 10 are not within the window range. However, when the window is shifted at the next time (after updating), the change points 9 and 10 fall within the window range.

  For each of the front end and the rear end of the moving direction of the window, it is managed whether the change point enters the window or the change point exits the window. The counting unit 13 can recognize the change point entering the window and the change point exiting the window based on the management table.

  Thus, the counting unit 31 can recognize the amount of change in the number of matches according to the change in the position of the window only by referring to the management table, and the magnitude of the data 1 and the data 2 after the change in the position of the window The number of matching relationships can be easily obtained.

  In the example of FIG. 13, the difference processing unit 15 recognizes the positional relationship between each change point and the window based on the time series data and the change point data. In the example of FIG. 13, the difference processing unit 15 manages a change point coming out from the rear end in the window and a change point located at the front end in the window using a table. This table is referred to as a management table.

  The management table is a table indicating the time (arrival time) to reach the front end in the window or the rear end outside the window for each change point. The arrival time indicates the number of times the window is shifted before reaching the front end in the window or the rear end outside the window.

  In the case of the example of FIG. 13, after the window is shifted, the change points 9 and 10 enter the window. Also, after the window is shifted, change points 1 and 2 exit from the window. Therefore, the difference processing unit 15 manages the change points No. 1, No. 2, No. 9, and No. 10 using the management table with the arrival time being zero.

  Therefore, the difference processing unit 15 can easily recognize a change point entering and exiting the window by managing the positional relationship between the window and each change point using the management table. The difference processing unit 15 obtains the amount of change in the number of matches after the window is shifted.

  At this time, when the window is shifted, the difference processing unit 15 can easily recognize the changing point entering and exiting the window only by referring to the management table, and can quickly determine the amount of change in the number of matches. it can.

<Example of similarity calculation for shifting one window>
Next, the calculation of the similarity when one of the data 1 and the data 2 is fixed and the other window is shifted will be described. As described above, the matching number P of the magnitude relationship between the data 1 and the data 2 before the window is shifted is “2”.

  When one of the windows is shifted, the counting unit 13 considers not only the amount of change in the coincidence number of the front end and the rear end in the moving direction of the window but also the positional relationship between the changing points in the window and the data 1 and The magnitude relationship with data 2 is counted.

  In the example of FIG. 14, the window for data 1 is fixed (fixed window), and the window for data 2 is shifted. Looking at the relative position in the window as a reference, each time the window is shifted, the relative positional relationship between the change point in the data 1 window and the change point in the data 2 window changes.

  Since the change point in the fixed window of data 1 is fixed, the change point in the window of data 2 may overtake the change point in the fixed window of data 1 in some cases. The counter 13 counts the magnitude relationship between the data 1 and the data 2 in consideration of this overtaking.

  The example of FIG. 15 shows a case where the amount of change in the number of coincidences in the magnitude relationship after the window of data 2 (hereinafter also referred to as a moving window) is shifted is “2”.

  In the case where one of the two data windows is fixed and one of the windows is shifted, the difference processing unit 15 adds a change point to the fixed window in order to count the number of coincidence in magnitude.

  As illustrated in the example of FIG. 16, the difference processing unit 15 sets three types of type A, type B, and type C for the fixed window. The difference processing unit 15 adds a change point to the fixed window according to the type. In the case of type C, the difference processing unit 15 does not add a change point.

  The type A range is set at the front end outside the fixed window, and the type B range is set at the rear end inside the fixed window. The type A range and the type B range are set to the same time difference range.

  For example, in the example of FIG. 16, the type A range is set to a time “7” in the Y direction, which is the front end outside the fixed window, and a time difference “1” to “4”. The range of type B is set to a time “2” in the X direction, which is the rear end of the fixed window, and a time difference “1” to “4”. Type C is set outside the range of type B in the fixed window.

  If there is no change point element in the type A range and the type B range, the difference processing unit 15 adds the element as a change point. At this time, the difference processing unit 15 adds the change point by inverting the magnitude relation of the element to which the change point is added.

  In the example of FIG. 16, there is no change point in the type A range, and there are two change points in the type B range. Therefore, the difference processing unit 15 reverses the magnitude relationship, adds four change points to the type A range, and adds two change points to the type B range.

  FIG. 17 shows an example of the amount of change in the number of matches when one window is shifted. The difference processing unit 15 weights the amount of change for each type described above. In the example of FIG. 17, the weight is “0” when the magnitude relationship matches in each element of the type A range, and the weight is “1” when the magnitude relationship does not match.

  The weight is “−1” when the magnitude relationship is the same in each element of the type B range, and the weight is “0” when the magnitude relationship is not the same. The weight is “−1” when the magnitude relationship is the same in each element of the type C range, and the weight is “1” when the magnitude relationship is not the same.

  In the example of FIG. 17, “anchor” indicates an element having a change point. The anchor also includes the added change point. In the example of FIG. 17, the difference processing unit 15 detects whether the magnitude relationship between the anchors in the fixed window of data 1 matches the magnitude relationship of the corresponding points in the window of data 2.

  In the example of FIG. 17, all four elements in the type A range have the same magnitude relationship, all four elements in the type B range do not have the same magnitude relationship, and all the two elements in the type C range The magnitude relationship does not match. The counting unit 13 obtains the amount of change in the number of coincidence in magnitude relation based on the weight. In the case of the example in FIG. 17, the amount of change in the number of coincidences in the magnitude relationship is “2 (= 0 + 0 + 2)”.

  Next, the weight of the change amount will be described with reference to the example of FIG. In the example of FIG. 18, light shading indicates a period in which the magnitude relationship is “−”, and dark shading indicates that the magnitude relationship is “+”.

  In Type A, when the magnitude relationship between data 1 and data 2 matches at the anchor position, the number of matches in the window does not increase or decrease even if the window of data 2 is shifted. Therefore, the weight of the change amount in this case is zero.

  In type A, when the magnitude relationship between data 1 and data 2 does not match at the anchor position, the number of matches in the window increases by one when the window of data 2 is shifted. Accordingly, the weight of the change amount in this case is “1”.

  In type B, when the magnitude relationship between data 1 and data 2 matches at the anchor position, the number of matches in the window decreases by one when the window of data 2 is shifted. Accordingly, the weight of the change amount in this case is “−1”.

  In Type B, if the magnitude relationship between data 1 and data 2 does not match at the anchor position, the number of matches in the window does not increase or decrease even if the window of data 2 is shifted. Therefore, the weight of the change amount in this case is zero.

  In type C, when the magnitude relationship between data 1 and data 2 matches at the anchor position, the number of matches in the window decreases by one when the window of data 2 is shifted. Accordingly, the weight of the change amount in this case is “−1”.

  In type C, if the magnitude relationship between data 1 and data 2 does not match at the anchor position, the number of matches in the window increases by one when the window of data 2 is shifted. Accordingly, the weight of the change amount in this case is “1”.

  FIG. 19 shows an example of the amount of change in the number of coincidences in magnitude relation after the window of data 2 is shifted. As shown in the example of FIG. 19, when the data 2 window is shifted, points in the data 2 window corresponding to two anchors of type B become change points.

  In this case, the difference processing unit 15 inverts the two anchors. In the case of the example of FIG. 19, the coincidence relationship between the two anchors was not coincident. The difference processing unit 15 inverts the coincidence relationship between the two anchors after the update (after the data window is shifted) to coincidence.

  In the example of FIG. 19, as a result of shifting the window of data 2, when the coincidence of the magnitude relations of corresponding points between data 1 and data 2 is reversed, the difference processing unit 15 is based on the weight for each type. , To obtain the amount of change in the number of matches in the magnitude relationship.

  As shown in the example of FIG. 19, when the type A anchor changes from matching to mismatching, the weight changes from zero to “1”, so the difference in change amount is “1”. When the type A anchor changes from match to mismatch, the weight changes from “1” to zero, so the difference in change amount is “−1”.

  When the type B anchor changes from matching to mismatching, the difference in change amount is “1” based on the change in weight. When the type B anchors are matched from the mismatch, the change amount difference is “−1” based on the change in the weight.

  When the type C anchor changes from matching to mismatching, the change amount difference is “2” based on the change in weight. When the type C anchors change from mismatch to match, the difference in change amount is “−2” based on the change in weight.

  The difference processing unit 15 obtains a difference in the change amount of each anchor. In the case of the example in FIG. 19, since the two type B anchors have changed from matching to mismatching, the difference processing unit 15 subtracts “−2 (= −1-1)” from the amount of change in the matching number of magnitude relationships. .

  As described above, since the amount of change in the number of matches before update (before shifting the window of data 2) was “2”, the difference processing unit 15 matches after update (after shifting the window of data 2). The number change amount “4 (= 2 − (− 2))” is obtained.

  Next, a management table in the case of shifting one of the windows will be described. As described above, the management table is a table that manages the positional relationship between the window and the change point. FIG. 20 shows an example of the management table when one window is shifted.

  The difference processing unit 15 assigns an address to each element of the anchor of data 1 and each change point of data 2. In the example of FIG. 20, the difference processing unit 15 assigns an alphabet to the address of each element of the anchor, and assigns a number to the address of each change point of the data 2.

  For example, “4-b” in the management table indicates that the address of the change point of data 2 is “4” and the address of the anchor is “b”. “4-b” before the update indicates an address before the window of data 2 is shifted.

When the window of data 2 is shifted, the difference processing unit 15 determines whether or not to change the anchor for the changing point that has entered the window. The difference processing unit 15 performs anchor replacement according to the following two criteria.
(1) When the change point entering the window corresponds to the previous anchor (2) When the change point immediately after the change point entering the window corresponds to the anchor of the change point

  In the case of the example of FIG. 20, there is no corresponding anchor before “b” in the address “4-b”. Therefore, the difference processing unit 15 determines that the above (1) is not satisfied. In addition, the change point immediately after the address “4-b” of the change point entering the window is “5”.

  However, the address “5” of the change point of data 2 corresponds to the anchor “i”. That is, the difference processing unit 15 manages the address “5” of the change point of the data 2 as “5-i” in the management table.

  Therefore, the anchor of the change point “4” is “b”, and the anchor of the next change point “5” is “i”, so the anchor does not correspond. For this reason, the difference processing unit 15 determines that the condition (2) is not satisfied.

<Description of various specific examples>
Next, three specific examples of calculating the similarity of time series data for the three time series data (data 1 to data 3) shown in the example of FIG. 21 will be described.

  Specific example 1 ((1) in FIG. 21) shows the similarity between data 1 and data 2, the similarity between data 1 and data 3, and the similarity between data 2 and data 3. This is an example of calculation. The period for which the similarity is calculated is from time “2” to “8”. The period for which the similarity is calculated is the window described above.

  In specific example 2 ((2) in FIG. 21), the time series data to be subjected to the calculation of the similarity is two data 1 and data 2. In the second specific example, the period for which the similarity is calculated is time “1” to “7” and time “4” to “10”.

  In the second specific example, the difference processing unit 15 obtains the amount of change in the number of matches while shifting the windows of both data 1 and data 2. And in the specific example 2, the calculating part 14 calculates the similarity (correlation value) of a total of 4 pairs.

  In specific example 3 ((3) in FIG. 21), the time series data that is the target of similarity calculation is data 1 and data 2. In the third specific example, the period for which the similarity is calculated is time “3” to “9” and time “4” to “10”.

  In the third specific example, the difference processing unit 15 fixes the window of the data 1 out of the data 1 and the data 2, and obtains the amount of change in the number of matches while shifting the window of the data 2. And in the specific example 3, the calculating part 14 calculates the similarity (correlation value) of a total of 4 pairs.

<Specific example 1>
FIG. 22 shows an example of change point detection when the time difference is “1”. In the time-series data shown in the example of FIG. 22, the values monotonically increase from time “1” to “3”, the values monotonously decrease from time “3” to “7”, and “7” to “10” The value decreases monotonously.

  Therefore, the time when the magnitude relationship of the values changes is “1”, “3”, “7”, and “10”. In the examples after FIG. 22, the solid arrow indicates a monotonically increasing section, and the broken arrow indicates a monotonically decreasing section.

  The detection unit 12 detects the change point in consideration of the time before the time in addition to the time when the magnitude relationship of the values changes. In the example of FIG. 23, the detection unit 12 includes the sections “1” to “2”, the sections “2” to “3”, the sections “3” to “6”, the sections “6” to “7”, and the sections A change point is detected as a section to be compared from “7” to “9”.

  In the example of FIG. 23, each of the above sections is described as “comparison source”, and “comparison source” is the Y direction of the matrix. Since the time difference is “1”, “comparison destination” is a time obtained by adding “1” to the time of “comparison source”. The “comparison destination” is the X direction of the matrix.

  FIG. 24 shows an example of the time difference between time “1” and time “2”. The value of time “1” is “2.1”, and the value of time “2” is “5.3”. The time difference between time “1” and time “2” is an initial value.

  Since the value of the time “1” is smaller than the value of the time “2”, the magnitude relationship between the time “1” and the time “2” is “−”. Therefore, the detection unit 12 detects “1” with the time difference “1”. In the example matrix of FIG. 24, a point where the time in the Y direction (comparison source) is “1” and the time in the X direction (comparison destination) is “2” is a change point of “−”.

  FIG. 25 shows an example of detection of a change point when the time between “1” and “2” is the comparison source and the time between “2” and “3” is the comparison destination. In this case, the value of the comparison source time “2” and the value of the comparison destination time “3” are the same.

  However, when there is one value that matches the comparison source and the comparison destination, the detection unit 12 considers that the comparison source section and the comparison destination section are separated. Accordingly, since the comparison source section and the comparison destination section are separated, the detection unit 12 does not detect the change point.

  FIG. 26 shows an example of change point detection when the comparison is made between time “2” and “3” and comparison is made between time “3” and “4”. In this case, the value “6.2” to the value “7.5” overlap in the comparison source section and the comparison destination section. Therefore, the detection unit 12 detects that the comparison source section and the comparison target section are not separated.

  Therefore, if there is a change point where the magnitude relationship changes in the above section, the detection unit 12 detects the change point. In the case of the example of FIG. 26, the magnitude relationship of values changes at time “3”. That is, since the value of time “2” is smaller than the value of time “3”, the magnitude relationship is “−”.

  On the other hand, since the value of time “3” is larger than the value of time “4”, the magnitude relationship is “+”. For this reason, the detection unit 12 detects that the magnitude relationship between the values has changed at time “3”. That is, the detection unit 12 detects time “3” as a change point. The detection unit 12 adds “3+” to the time difference “1” in the change point data.

  Next, as shown in the example of FIG. 27, the detection unit 12 has a magnitude relationship between the comparison source time “3” to “6” and the comparison target time “4” to “7”. If there is a changing point that changes, the changing point is detected.

  The section from time “3” to “6” of the comparison source and the section from time “4” to “7” of the comparison destination are monotonously decreasing sections. Therefore, there is no change point in this monotonically decreasing section. Therefore, the detection unit 12 skips the detection of change points in the same monotonically decreasing section.

  FIG. 28 shows an example of detection of a change point in the case where the time “6” to “7” is the comparison source and the time “7” to “8” is the comparison destination. Since the comparison source section and the comparison destination section have overlapping values, the detection unit 12 detects that the comparison source section and the comparison destination section are not separated.

  Therefore, if there is a change point where the magnitude relationship changes in the above section, the detection unit 12 detects the change point. In the case of the example of FIG. 28, it is detected that the magnitude relationship between the values has changed at time “7”. The detection unit 17 adds “7−” to the time difference “7” in the change point data.

  In the example of FIG. 29, the section from time “7” to “9” of the comparison source and the section from time “8” to “10” of the comparison destination are monotonically increasing sections. Therefore, there is no change point in this monotonically increasing section. Therefore, the detection unit 12 skips the detection of change points in the same monotonically increasing section.

  Next, detection of a change point when the time difference is “2” will be described. As shown in the example of FIG. 30, the time when the magnitude relationship of the values changes is “1”, “3”, “7”, and “10”.

  Since the time difference is “2”, “the time at which one is inverted” is times “−1”, “1”, “5”, and “8” obtained by subtracting “2” from each of the above times. Therefore, the comparison source section and the comparison destination section are sections shown in the example of FIG.

  When the time difference is “2”, the time difference of the time for which the magnitude relation of the values is compared is “2”. For example, in the example of FIG. 31, the detection unit 12 compares the magnitude relationship between the values of time “1” and time “3”.

  In this case, since the value of time “1” is smaller than the value of time “3”, the magnitude relation is “−”. The detection unit 12 adds “1” to the initial value of the time difference “2”. Note that the detection unit 12 adds the change point data of the time difference “2” to the change point data for which the process for the time difference “1” has been completed.

  FIG. 32 shows an example of detection of a change point when the time “1” to “3” is the comparison source and the time “3” to “5” is the comparison destination. Values overlap in the comparison source section and the comparison destination section. Therefore, if there is a change point in this section, the detection unit 12 detects the change point.

  The detection unit 12 may divide a section in which a change point is detected. In the example of FIG. 32, the detection unit 12 divides the above section into two, and detects a change point in each section. When the section is large, it may be more efficient for the detection unit 12 to detect the change point from the divided small-sized section than to detect the change point from one section.

  In the example of FIG. 32, the detection unit 12 divides the above-described section into two sections. The first section is a section in which the comparison source time is “1” to “2” and the comparison destination time is “3” to “4”. The second section is a section in which the comparison source time is “2” to “3” and the comparison destination time is “4” to “5”.

  In the first section, there is no change in the magnitude relationship between the values, so the detection unit 12 does not detect the change point. In the second section, the magnitude relationship of values changes at time “3”. For this reason, the detection part 12 detects a change point in the 2nd area. Therefore, the detection unit 12 adds “3+” to the change point data of the time difference “2”.

  FIG. 33 shows an example of detection of a change point when the time “3” to “5” is the comparison source and the time “5” to “7” is the comparison destination. Since this section is a monotone decreasing section, there is no change point. Therefore, the detection unit 12 skips the detection of change points in the same monotonically decreasing section.

  FIG. 34 shows an example of detection of a change point when the time “5” to “7” is the comparison source and the time “7” to “9” is the comparison destination. In this interval, values are not separated. Therefore, if there is a change point in this section, the detection unit 12 detects the change point.

  In the example of FIG. 34, the detection unit 12 divides the above section into two. In the first section, the comparison source is between time “5” and “6”, and the comparison destination is between time “7” and “8”. In the second section, the time between “6” and “7” is the comparison source, and the time between “8” and “9” is the comparison destination.

  In the first section, the magnitude relationship between values does not change. Therefore, the detection unit 12 does not detect a change point from the first section. In the second section, the magnitude relationship of values changes at time “7”. The detection unit 12 detects the time “7” as a change point, and adds “7−” to the change point data of the time difference “2”.

  FIG. 35 shows an example of detection of a change point when the time “7” to “8” is the comparison source and the time “9” to “10” is the comparison destination. Since this section is the same monotonically increasing section, the detection unit 12 does not detect a change point. Therefore, detection of the change point is skipped.

  The detection unit 12 repeats the above-described processing from the time difference “3” to “9”. Thereby, the detection part 12 produces | generates change point data as shown by the example of FIG. The counting unit 13 counts the number of coincidence of magnitude relationships based on the change point data, and the calculation unit 14 calculates the similarity between the two time series data.

  For example, when all the magnitude relationships for each time difference are stored for each time-series data to be compared, the amount of information on the magnitude relationship to be stored increases. For this reason, it takes a long time to process the number of coincidences of the magnitude relationship, and the calculation time of the similarity also becomes long.

  Further, when all the magnitude relationships of values for each time difference are stored for each time series data to be compared, the amount of information to be stored increases.

  As described above, the detection unit 12 stores the change point of the time series data in the storage unit 11. The counting unit 13 counts the number of matches in magnitude relation based on the change point, and the calculation unit 14 calculates the similarity between the time series data based on the number of matches P in magnitude relation.

  Since the calculation unit 14 calculates the degree of similarity between the time series data using the number of coincidence P of the magnitude relationship counted based on the change point of the magnitude relationship, the calculation unit 14 calculates based on all the magnitude relationships for each time difference. Compared with the case of performing, the information to be calculated is reduced. For this reason, the calculation time for calculating the similarity is shortened.

  Compared with the case where all the magnitude relationships for each time difference of the time series data are stored, the amount of information to be stored is smaller when the change point data indicating only the change points of the magnitude relationship is stored. Furthermore, since the detecting unit 12 skips the same monotonically increasing section, the same monotonically decreasing section, and the like and detects the changing point, it can quickly detect the changing point.

  FIG. 37 shows an example of change point data of data 2 and data 3. As in the case of the data 1 described above, the detection unit 12 detects the change points of the data 2 and the data 3 and stores the change point data in the storage unit 11.

  Next, the number of matches in the magnitude relationship between data 1 and data 2 from time “2” to “8” will be described. FIG. 38 shows an example of change point data of data 1 and data 2 and respective matrices.

  When the counting unit 13 counts the number of coincidence of the magnitude relationship between the data 1 and the data 2 from the time “2” to “8”, the window range is “7”. Therefore, as shown in the example of FIG. 39, the target of counting the number of matches is between the time differences “1” to “6”.

  Data 1 is represented as “D1”, and data 2 is represented as “D2”. The counting unit 13 obtains an offset so that the end of the window becomes “1” in order to count the number of coincidence of the magnitude relationship between the data 1 and the data 2.

  Since the window of data 1 and data 2 starts from time “2”, the offset of data 1 and the offset of data 2 are both “1 (= 2-1)”. As described above, when the time difference is “1”, the window range is changed from the time “1” to “6 (= 7-1)”.

  As shown in the example of FIG. 40, a table indicating a change point for each of two time-series data to be subjected to similarity calculation is referred to as a change point table. Information on change points is stored in each item of the change point table. A value obtained by subtracting the offset value from the change point value may be stored in parentheses of each item.

  In the example of FIG. 40, a matrix of data 1 and data 2 is shown. In the example of FIG. 40, the position corresponding to the Y direction of the change point according to the time difference is shown between the two matrices. The alternate long and short dash line indicates the window range.

  FIG. 41 shows an example of comparison between the change point “1-” of data 1 and the change point “1-” of data 2. The change point “1-” of data 1 and data 2 is out of the window range. In the example of FIG. 41, two change points surrounded by a dotted line between two matrices are a change point “1-” of data 1 and a change point “1-” of data 2.

  These two change points are out of the window range to be counted for the number of coincidence in magnitude relation. Therefore, the counting unit 13 does not determine whether the magnitude relations coincide with each other regarding these two change points. That is, the number of matches at the time of the example in FIG. 41 is “0”.

  In addition, the counting unit 13 subtracts the offset value from the change point value in parentheses of the change point “1-” item of data 1 and the change point “1-” item of data 2 in the change point table. Store the stored value.

  FIG. 41 shows an example of comparison between the change point “1-” of data 1 and the change point “1-” of data 2. The change point “1-” of data 1 and data 2 is out of the window range. In the example of FIG. 41, two change points surrounded by a dotted line between two matrices are a change point “1-” of data 1 and a change point “1-” of data 2.

  These two change points are out of the window range to be counted for the number of coincidence in magnitude relation. Therefore, the counting unit 13 does not determine whether the magnitude relations coincide with each other regarding these two change points. That is, the number of matches at the time of the example in FIG. 41 is “0”.

  When the processing for the number of coincidence in magnitude relation is completed, the counting unit 13 moves the comparison target to the change point with the lowest index value among the change points in the change point table. Therefore, the change point to be compared next is the change point “2+”.

  FIG. 42 shows an example of comparison between the change point “1-” of data 1 and the change point “2+” of data 2. The change point “1-” of data 1 is out of the window range. Therefore, the number of matches at the time of the example of FIG. 42 is “0”.

  Next, the change point to be compared is the change point “3+” for the data 1 and the change point “3-” for the data 2. These two change point indexes have the same value. In this case, the counting unit 13 moves the change point of the data 1 and the change point of the data 2 together.

  FIG. 43 shows an example of comparison between the change point “3+” of data 1 and the change point “3-” of data 2. The counting unit 13 counts the number of coincidence of the magnitude relation for each of the data 1 and the data 2 based on the magnitude relation at the change point.

  In the example of FIG. 43, the offset of the change point “3+” of data 1 is “2”, and the offset of the change point “3-” of data 2 is “2”. The magnitude relationship between the two does not match. Therefore, the number of matches at the time of the example of FIG. 43 is “0”.

  The example of FIG. 44 illustrates a case where the comparison target of data 1 is moved to the next change point “7−”. The offset of the change point “7−” of data 1 is “6”, and the magnitude relationship before the offset “6” in the window range is “−”.

  The offset of the change point “3-” of data 2 is “2”, and the magnitude relationship after the offset “2” in the window range is “−”. Therefore, the magnitude relationship between the data 1 and the data 2 matches at the offset “6”.

  For this reason, the counting unit 13 adds the number of matches in magnitude relation. Since the initial value of the number of matches in the magnitude relationship is zero, the number of matches in the magnitude relationship at this time is “1”.

  As shown in the example of FIG. 45, the counting unit 13 moves the comparison target of the data 2 to the next change point “8+”. At this point, the comparison of the magnitude relationship between data 1 and data 2 within the window range has been completed. Accordingly, the counting unit 13 sets the number of matches as zero, and ends the process of counting the number of matches in the magnitude relationship at the time difference “1”.

  Next, the number of coincidence of magnitude relations when the time difference is “2” will be described. In the example of FIG. 46, since the time difference is “2”, the window range is between “1” and “5”.

  FIG. 47 shows an example of comparison between the change point “1-” of data 1 and the change point “1-” of data 2. These two changing points are out of the window range. Therefore, the counting unit 13 does not determine whether the magnitude relations coincide with each other regarding these two change points. That is, the number of matches at the time of the example of FIG. 47 is “0”.

  As shown in the example of FIG. 48, the offset of the change point “3+” of data 1 and the change point “3-” of data 2 is the same. The counting unit 13 moves the comparison target to the change point “3+” of the data 1 and the change point “3-” of the data 2.

  The offset of the change point “3+” of data 1 is “2”, and the magnitude relationship before the offset “2” in the window range is “+”. The offset of the change point “3-” of data 2 is “2”, and the magnitude relationship before the offset “2” in the window range is “−”.

  Therefore, the magnitude relationship between the two does not match. The counting unit 13 does not add the number of matches in magnitude relation. Since the initial value of the number of matches in the magnitude relationship at the time difference “2” is zero, the number of matches in the magnitude relationship at this time is zero.

  As shown in the example of FIG. 49, the index of the change point “7−” of data 1 and the change point “7+” of data 2 are the same. The counting unit 13 moves the comparison target to the change point “7−” of data 1 and the change point “7+” of data 2.

  The magnitude relationship from the change point “3+” to the change point “7−” of data 1 is “−”. The magnitude relationship from the change point “3-” to the change point “7+” in data 2 is “+”. Therefore, since the magnitude relationship between the two does not match, the counting unit 13 does not add the number of matches in the magnitude relationship.

  Accordingly, since the number of coincidence of the magnitude relationship at this time is zero, the number of coincidence at the time difference “2” is zero, and the processing is ended.

  As described above, the counting unit 13 counts the number of matches in the magnitude relationship between the data 1 and the data 2 for the time difference “1” and the time difference “2”. As described above, the count of the number of coincidence in the magnitude relationship is performed based on the change point in the magnitude relationship.

  The counting unit 13 counts the number of coincidences of the magnitude relationship from the time differences “3” to “7”, similarly to the time differences “1” and “2”. As described above, the period for which the similarity between data 1 and data 2 is calculated is a period between times “2” and “8”.

  The counting unit 13 sums up the number of matches for each time difference. In the case of the example in FIG. 50, the counting unit 13 obtains that the coincidence number P between the data 1 and the data 2 between the times “2” and “8” is “1”.

  The calculation unit 14 uses the coincidence number P counted by the counting unit 13 and the data size of the time-series data (number of items = n) to calculate the times “2” and “8” according to the above equation (A). The similarity (correlation value) between data 1 and data 2 is calculated.

  The number of matches P is “P = 1”, and the number of items n is “n = 7” because it is the number of times (items) in the window range from time “2” to “8”. Therefore, the calculation unit 14 performs calculation using the above-described formula (A) to obtain a similarity “t = (4 × 1/7 × (7-1)) − 1”. The calculation result is approximately “−0.90”.

  Therefore, the similarity (correlation value) between data 1 and data 2 in the window range is about “−0.90”.

  In the first specific example, the calculation unit 14 calculates not only the similarity between the data 1 and the data 2 but also the similarity between the data 1 and the data 3 and the similarity between the data 2 and the data 3.

  As shown in the example of FIG. 51, the total value of the number of coincidence of the magnitude relationships for each time difference between the data 1 and the data 3 in the window range is “11”. The calculation unit 14 performs the calculation of Expression (A) using the number of matches P (P = 11) and the number of items n (n = 7). The calculation result (similarity t) is about “−0.05”.

  A value obtained by summing up the number of coincidence of magnitude relations for each time difference between data 2 and data 3 in the window range is “9”. The calculation unit 14 performs the calculation of Expression (A) using the number of matches P (P = 9) and the number of items n (n = 7). The calculation result (similarity t) is about “−0.14”.

  Therefore, three sets of similarities of two time-series data pairs of data 1, data 2, and data 3 are obtained.

<Specific example 2>
Specific example 2 is an example in which the similarity between two time series data is calculated while shifting both windows in the two time series data to be compared. In the example of FIG. 52, the change point table includes items of order. The order indicates the order of the change points to be compared.

  In the specific example 2, the difference processing table shown in the example of FIG. 52 is used. The difference processing table includes items of time difference, number of matches, rear end match, front end match, next rear end, and next front end.

  The time difference indicates a time difference to be subjected to difference processing. The number of matches indicates the number of matches of two time series data according to the time difference. The rear end coincidence indicates whether the magnitude relationship between the two time-series data at the rear end outside the window coincides. The coincidence of the front end indicates whether or not the magnitude relationship between the two time series data at the front end in the window coincides.

  The next trailing edge indicates the transition point that emerges from the trailing edge of the window after the window is shifted. The next front edge indicates the transition point that enters the next window after the window is shifted.

  In the example of FIG. 53, the counting unit 13 counts the number of coincidence of magnitude relations for the change point “1-” of data 1 and the change point “1-” of data 2. Data 1 is time “1” and the magnitude relationship is inverted to “−”. Data 2 also reverses the magnitude relationship to “−” at time “1”.

  Therefore, since the magnitude relationship between data 1 and data 2 matches, the counting unit 13 adds the number of matches. As a result, the number of matches becomes “1”. The difference processing unit 15 sets the number of matches in the difference processing table to “1”.

  The change point “1-” of data 1 and the change point “1-” of data 2 are located at the rear end outside the window because the offset is “1” in the change point table. The magnitude relationship between the two change points is “−”.

  Therefore, the difference processing unit 15 sets the matching item at the rear end to “◯”. Further, the change point “1-” of data 1 and the change point “1-” of data 2 come out of the window when the window is shifted.

  The difference processing unit 15 stores information indicating the two change points in the next item in the change point table. In the example of FIG. 53, the information indicating the change point includes information on the data number, the order, and the arrival time.

  The data number indicates a number that identifies time-series data. For example, “D1” indicates data 1. The order indicates the order of the change point table.

  The arrival time in parentheses indicates the time until the change point comes out of the window. When the window is shifted once, the time shifts backward by one. For example, when the arrival time is “1”, when the window is shifted once, the change point indicates that the window comes out of the window.

  For example, in the example of FIG. 53, the information “D1-1 (1)” indicating the change point indicates that the change point is the change point of the data 1. In addition, the order of the change points is “1”, and when the window is shifted once, the change points come out of the window.

  Next, the comparison target of data 2 moves to the change point “2+”. The processing for determining whether or not the magnitude relationship between two time-series data in the window matches is the same as in the first specific example. As shown in the example of FIG. 54, the number of matches does not change.

  Further, since the windows are not shifted, there is no change in the rear end coincidence and the next rear end. Therefore, as shown in the example of FIG. 54, there is no change in the contents of the difference processing table.

  Next, as shown in the example of FIG. 55, the comparison target of data 1 moves to the change point “3+”, and the comparison target of data 2 moves to the change point “3-”. In this case, since the two change points have the same offset, both the change point of data 1 and the change point of data 2 move to the next.

  Since the windows are not shifted and the number of matches does not change, the content of the difference processing table does not change.

  Next, as shown in the example of FIG. 56, the comparison target of data 1 moves to the change point “7−”. Since the window is not shifted and the number of matches does not change, the time difference, the number of matches, the rear end match, and the information of the next rear end item in the difference processing table do not change.

  The difference processing unit 15 determines whether or not the front end of the data 1 matches the front end of the data 2 because the change point “7−” to be compared with the data 1 comes out of the window. Since the data 2 has not reached the front end of the window, the difference processing unit 15 sets “X” as the matching item at the front end in the difference processing table.

  When the window is shifted, the change point “7−” of data 1 enters the window. The information indicating the change point stored at the next front end includes information on the data number, the order, and the arrival time. These pieces of information are the same as the information indicating the change point stored at the next rear end.

  In the case of the change point “7−” of data 1, the data number is “D1”, the order is “3”, and the arrival time is “1”. Therefore, the difference processing unit 15 stores the information “D1-3 (1)” in the next front end item in the difference processing table.

  Next, as shown in the example of FIG. 57, the comparison target of the data 2 moves to the change point “8+”. Since the window is not shifted and the number of matches does not change, the time difference, the number of matches, the rear end match, and the information of the next rear end item in the difference processing table do not change.

  The magnitude relation of data 1 at the front end of the window is “+”, and the magnitude relation of data 2 is “−”. Therefore, the size relationship between data 1 and data 2 does not match at the front end of the window. The difference processing unit 15 sets “x” as the matching item at the front end in the difference processing table.

  When the window is shifted twice, the change point “8+” of data 2 enters the window. Therefore, the difference processing unit 15 adds “D2-4 (2)” to the next front end item in the difference processing table.

  As described above, the difference processing unit 15 generates a difference processing table when the time difference is “1”. The difference processing unit 15 performs the same processing as when the time difference is “1”, and generates a difference processing table when the time difference is “2” to “6”.

  FIG. 58 shows an example of the generated difference processing table. The counting unit 13 sums up the number of matches in the magnitude relationship from the time difference “1” to “6” to obtain the number of matches P (P = 4). The calculation unit 14 performs calculation by fitting “P = 4” and “n = 7” to the above-described formula (A) to obtain a similarity (correlation value) t (t = −0.62).

  The difference processing unit 15 sums up the number of “◯” of the matching items at the front end based on the difference processing table of the time differences “1” to “6”. In the case of the example in FIG. 58, the total number of “O” s corresponding to the front end is “1”. Further, the difference processing unit 15 sums up the number of “◯” of the matching items at the rear end. In the case of the example in FIG. 58, the total number of “o” s corresponding to the trailing ends is “4”.

  The difference processing unit 15 subtracts the sum of the number of matching “◯” at the rear end from the sum of the number of matching “◯” at the front end. In the example of FIG. 58, the subtraction result is “−3”. This subtraction result is the amount of change in the number of matches (may be referred to as a change in the number of matches after FIG. 58).

  If the change point of the magnitude relationship does not enter or exit from the window when the window is shifted, the amount of change in the number of matches is constant. On the other hand, when the change point of the magnitude relationship enters and exits from the window when the window is shifted, the amount of change in the number of matches changes.

  Next, an example of the management table in specific example 2 will be described. The difference processing table shown in the example of FIG. 59 is a table in which the items of the number of matches, the number of matches at the rear end, and the match at the front end are omitted from the difference processing table shown in the example of FIG.

  The management table includes items of arrival time, rear end, and front end. The management table is a table showing the positional relationship of change points with respect to the window. In the rear end item, information indicating a change point is stored for each time until the rear end is reached. In the front end item, information indicating a change point is stored for each time until the front end is reached.

  The difference processing unit 15 generates a management table based on the information indicating the change point stored in the next rear end and the next front end of the difference processing table and the time difference. Information indicating a change point stored in the management table includes information on a time difference, a data number, and an order.

  For example, in the example of FIG. 59, the information indicating the change point of the next rear end item in the time difference “4” is “D1-3 (3)”. Among these, “D1” indicates the data number, “3” indicates the order, and “3” in parentheses indicates the arrival time.

  The difference processing unit 15 extracts each change point from the difference processing table, and stores each change point in the management table according to the arrival time in parentheses. For example, when the information indicating the next front end change point is “D1-3 (3)”, the difference processing unit 15 indicates the change point in the front end item of the management table arrival time “3”. Is stored.

  In the example of FIG. 59, the difference processing unit 15 converts information indicating a change point into information including a time difference, a data number, and an order, and stores the information in the management table. For example, when the information indicating the next front end change point is “D1-3 (3)”, the time difference is “4”, the data number is “D1”, and the order is “3”.

  The difference processing unit 15 stores information indicating the change point in the form of “4-D1-3” in the front end item of the arrival time “3” in the management table. The difference processing unit 15 performs the same processing on information indicating each change point stored in the difference processing table, and stores a management table as illustrated in the example of FIG.

  The example of FIG. 60 shows an example when the windows of both data 1 and data 2 are shifted. In this case, the difference processing unit 15 increments the arrival time of the management table in the example of FIG. 59 by one and increments the offsets of the data 1 and the data 2. In the example of FIG. 60, the offset value of data 1 and data 2 is “1”.

  FIG. 61 shows an example in which the difference processing unit 15 updates the management table. As the window of data 1 shifts, the change point “1-” (represented by “1-D1-1” in the management table) at the time difference “1” comes from the rear end of the window.

  Since the change point “1-” at the time difference “1” comes out of the window, the difference processing unit 15 inverts the coincidence of the trailing edge of the window at the time difference “1” in the difference processing table. In the example of FIG. 61, the coincidence of the trailing edges of the window at the time difference “1” is “◯”, and therefore the difference processing unit 15 inverts “◯” to “×”.

  As described above, the amount of change in the number of matches is a value obtained by subtracting the total value of the number of matching “O” at the rear end from the total value of the number of matching “O” at the leading end in the difference processing table. The amount of change in the number of matches before the window was shifted was “−3”.

  When “◯” in the matching at the rear end is inverted to “×”, the amount of change in the number of matches increases. In the case of the example of FIG. 61, the match at the rear end at the time difference “1” has changed to “x”, and thus the amount of change in the number of matches increases by one.

  The next change point after the change point “1-” in the time difference “1” is “3+”. This change point “3+” becomes the next rear end. The difference processing unit 15 stores the change point “3+” in the management table.

  The change point “3+” is a change point of the data 1, the time difference is “1”, and the order is “2”. The difference processing unit 15 stores information indicating the change point “3+” in the form of “1-D1-2” at the rear end of the management table.

  FIG. 62 shows an example of updating the management table when attention is paid to the change point “2+” in the time difference “6” of the data 1. As the window shifts, a change point “2+” (represented by “6-D1-2” in the management table) in the time difference “6” of data 1 enters from the front end of the window.

  When the window shifts, the change point “−1” of the time difference “6” comes out of the window. Therefore, the next rear end in the time difference “6” of the data 1 is the change point “2+”. The time (arrival time) until the change point “2+” reaches the rear end of the window is “1”.

  The difference processing unit 15 moves “6-D1-2” from the front end to the rear end of the management table. Further, since the change point “2+” at the time difference “6” of the data 1 has entered the window, the difference processing unit 15 inverts the coincidence of the front end at the time difference “6” of the difference processing table.

  Since the match at the front end at the time difference “6” is inverted to “x”, the amount of change in the number of matches is reduced by one. Therefore, the amount of change in the number of matches is “−3 (= −3 + 1−1)”.

  The difference processing unit 15 performs the above-described processing for all the change points in which the arrival time is zero in the management table. FIG. 63 shows an example of a management table that has been processed for all change points whose arrival time is zero. The difference processing unit 15 deletes the processed change point from the management table.

  The difference processing unit 15 updates the rear end match and the front end match of the difference processing table. In the example of FIG. 63, for example, the coincidence of the trailing edge of the time difference “1” is inverted twice and thus is not updated.

  By shifting the window, the change point “1−” of the time difference “1” of the data 1 comes out of the window. Thereby, in the difference processing table, the match at the rear end of the change point is reversed.

  Further, the change point “1−” of the time difference “1” of the data 2 also comes out of the window by shifting the window. Thereby, in the difference processing table, the match at the rear end of the change point is reversed.

  Accordingly, in the difference processing table, the match at the trailing edge of the time difference “1” is inverted twice. In this case, the difference processing unit 15 does not update the matching at the trailing edge of the time difference “1”. .

  In the case of the example in FIG. 63, the sum of the number of matching “O” at the front end and the sum of the number of matching “O” at the rear end in the difference processing table do not change. Therefore, the amount of change in the number of matches after the window is shifted (after update) is “−3”.

  As shown in the example of FIG. 64, the difference processing unit 15 adds the amount of change “−3” of the number of matches to the number of matches “4” before the window is shifted. As a result, the number of matches in the magnitude relationship between the data 1 and the data 2 after the window is shifted is “1 (= 4-3)”.

  The calculation unit 14 calculates the number of matches P (P = 1) and the number of items (n = 7) by applying the above formula (A), and as a calculation result, the similarity “t” after the window is shifted. = −0.90 ”.

  FIG. 65 shows an example of calculating the similarity (correlation value) when the window is shifted. Since the window is shifted, the offset of the change point data is increased by one. The amount of change in the number of matches before the window is shifted is “−3”.

  In the difference processing table, the match of the front end at the time difference “3” and the match of the front end at the time difference “1” are reversed. Since both are reversed in the opposite direction, when only focusing on the coincidence at the front end, the amount of change in the coincidence number is zero.

  In the coincidence at the rear end of the difference processing table, the four time differences “1”, “4”, “5”, and “6” change from “◯” to “X”. Therefore, the amount of change in the number of matches increases by four. Since the amount of change in the number of matches before the window is shifted is “−3”, the amount of change in the number of matches after the window is shifted is “1 (= −3 + 4)”.

  The difference processing unit 15 adds the change number “1” of the number of matches to “1” as the number of matches before the window is shifted to obtain the number of matches P (P = 2).

  The calculation unit 14 calculates the similarity t by fitting the number of matches P (P = 2) and the number of items n (n = 7) to the above-described formula (A). Thereby, the calculation unit 14 obtains the similarity “t = −0.81”.

  Next, FIG. 66 shows an example of similarity calculation when the window is shifted. The difference processing unit 15 updates the offset of data 1 and data 2 to “3” because the window is shifted.

  In the example of FIG. 66, the coincidence of the leading ends in the time differences “1” and “4” in the difference processing table is inverted to “◯”.

  Therefore, the difference processing unit 15 adds “2” to the change amount “1” before the window is shifted to obtain the change amount “3” of the number of matches. Since the number of matches before the window is shifted is “2”, the difference processing unit 15 adds “3” to “2” to obtain the number of matches P (P = 5).

  The calculation unit 14 calculates the similarity t by fitting the number of matches P (P = 5) and the number of items n (n = 7) to the above-described equation (A). Thereby, the calculation unit 14 obtains the similarity “t = −0.52”. Since the window has been shifted to the end of data 1 and data 2, the processing is completed.

<Specific example 3>
Next, an example of similarity calculation when the window of one time series data is fixed and the window of the other time series data is shifted among the two time series data to be subjected to similarity calculation will be described. To do.

  In the example of FIG. 67, it is assumed that time “3” to “9” of the change point data of data 1 is the window range. As illustrated in the example of FIG. 67, the difference processing unit 15 performs the following processing as an offset “2 (= time“ 3 ”−time“ 1 ”)”.

  The window for data 1 is fixed. The change point “1-” of the time difference “1” is not in the window. In the change point table, the next change point “3+” is located at the rear end in the window. Therefore, the anchor of the change point “3+” is type B.

  The difference processing unit 15 adds the information on the change point “3+” to the data related to the anchor (hereinafter, anchor data). The difference processing unit 15 adds “1” in parentheses, which is an offset of the change point “3+”, information specifying type B, and information having a magnitude relationship of “+” to the anchor data. . In the example of FIG. 68, this information is “B1 +”.

  In the example of FIG. 69, the change point “7−” is located at a location other than the rear end in the window. Therefore, the anchor of the change point “7−” is type C, and the offset is “5”. The difference processing unit 15 adds “C5-” to the anchor data.

  The difference processing unit 15 determines whether there is a change point at the front edge of the window for the time difference “1”. The last change point in the change point table is “7−”. Therefore, in the example of FIG. 70, there is no change point at the front edge of the window.

  In this case, as described above, the difference processing unit 15 adds a change point. Since the time at the front edge of the window is “10”, the offset is “7”. The magnitude relationship at time “10” is “+”. Therefore, the difference processing unit 15 adds “A7 +” to the anchor data.

  FIG. 71 shows an example of anchor data from the time difference “1” to “6”. The difference processing unit 15 performs the same processing as in the case of the time difference “1”, and generates anchor data from the time difference “2” to “6”. Anchor data for each time difference is information of a fixed window in data 1.

  Next, an example of the number of matches in the magnitude relationship between data 1 and data 2 will be described. In Specific Example 3, when data 1 and data 2 are compared, the difference processing unit 15 uses an anchor table for data 1 and a change point table for data 2.

  In the case of the example of FIG. 71, the window range of the data 2 is from time “1” to “7”. On the other hand, the window range of data 1 is from “3” to “9”. As described above, the difference processing unit 15 generates anchor data of data 1 in consideration of the offset “2”.

  In the example of FIG. 72, the comparison target is the anchor “B1 +” for data 1 and the change point “1-” for data 2. The anchor “B1-” corresponds to the change point “3” in the data 1 as described above.

  In the example of FIG. 72, the difference processing unit 15 generates an anchor table. The anchor table includes information on the number of matches, the matching relationship between the anchors, and the change point that reaches the anchor next, according to the time difference.

  The anchor correspondence relationship indicates whether or not the magnitude relationship between the anchor of data 1 to be compared and the change point of data 2 matches. In the example of FIG. 72, the matching relationship between anchors indicates whether or not they match for each anchor order.

  The magnitude relationship between the anchor “B1 +” and the change point “1-” is opposite. Since the magnitude relationship between the data 1 and the data 2 does not match in the anchor “B1-”, the difference processing unit 15 sets the number 1 in the anchor table to “x”. Further, since the magnitude relationship between the anchor “B1 +” and the change point “1-” does not match, the counting unit 13 does not add the number of matches in the magnitude relationship.

  The example of FIG. 73 shows a case where the comparison targets are the anchor “B1 +” of data 1 and the change point “2+” of data 2. The magnitude relationship from the change point “1+” of data 1 to the change point “2+” of data 2 is “+”, which matches the magnitude relationship of the anchor “B1 +” of data 1. Therefore, the difference processing unit 15 adds the number of coincidence in magnitude relation.

  The change point “2+” of data 2 is located at the rear end of the window when the window is shifted. The difference processing unit 15 stores the information of the change point “2+” of the data 2 in “change point that reaches the anchor next” in the anchor table.

  The difference processing unit 15 includes information indicating the order of the change points of the data 2, information on the number of times (time) the window is shifted before the change points reach the anchor (in this case, the rear end in the window), and The information indicating the order of the corresponding anchors is stored in the anchor table.

  In the example of FIG. 73, the information indicating the order of the data change point “2+” is “2”. The change point “2+” reaches the anchor when the window is shifted once. Since the corresponding anchor is “B1 +”, the information indicating the order of the corresponding anchor is “1”.

  The difference processing unit 15 stores “2 (1) −1” as information indicating the change point “2+” in “change point that reaches the anchor next” in the anchor table. The value in parentheses indicates the number of times the window is shifted before the above change point reaches the anchor.

  The example of FIG. 74 shows a case where the comparison targets are the anchor “B1 +” of data 1 and the change point “3-” of data 2. The magnitude relationship from the change point “2+” of data 1 to the change point “3-” of data 2 is “−”, which does not match the magnitude relationship of the anchor “B1 +” of data 1. Therefore, the difference processing unit 15 does not add the number of coincidence in magnitude relation.

  As shown in the example of FIG. 75, the difference processing unit 15 moves the comparison target to the anchor “C5-” of data 1 and the change point “3-” of data 2. The magnitude relationship from the change point “2+” of data 1 to the change point “3-” of data 2 is “−”, which matches the magnitude relationship of the anchor “C5-” of data 2. Therefore, the difference processing unit 15 adds the number of coincidence in magnitude relation.

  In the anchor “C5-” of data 1, the anchor “C5-” and the change point “3-” have the same magnitude relationship. Therefore, the difference processing unit 15 sets the second “anchor matching relationship” to “◯”.

  As shown in the example of FIG. 76, the difference processing unit 15 moves the comparison target to the anchor “A7 +” of data 1 and the change point “3-” of data 2. The magnitude relationship from the change point “2+” of data 1 to the change point “3-” of data 2 is “−”, which matches the magnitude relationship of the anchor “B1 +” of data 1. Therefore, the difference processing unit 15 adds the number of coincidence in magnitude relation.

  Further, in the anchor “A7 +” of the data 1, the anchor “A7 +” does not coincide with the change point “3-”. Therefore, the difference processing unit 15 sets the third “anchor matching relationship” to “x”.

  As shown in the example of FIG. 77, when the window is shifted, the change point “8+” of data 2 is located at the front end of the window. The difference processing unit 15 stores the information of the change point “8+” of the data 2 in “change point that reaches the anchor next” in the anchor table.

  The information indicating the order of the change point “8+” of data 2 is “4”, and the number of times the window is shifted before the change point reaches the anchor (in this case, the front end of the window) is “1”. The corresponding anchor order is “3”. Therefore, the difference processing unit 15 adds “4 (1) -3” to “the changing point that reaches the anchor next”.

  Thus, the process for the time difference “1” is completed. The difference processing unit 15 performs the same processing as the time difference “1” for the time differences “2” to “6”. FIG. 78 shows an example of an anchor table for each time difference.

  In the example of FIG. 79, the difference processing unit 15 uses the information of each change point stored in “change point that reaches the anchor next” in the anchor table in order of the number of times that the window is shifted before reaching the anchor (time (In order).

  The difference processing unit 15 manages the information of each change point in the order of arrival time, with the arrival time being the number of times the window is shifted among the information of each change point of “the next change point reaching the anchor” in the anchor table. To store.

  In the example of FIG. 79, the difference processing unit 15 stores information on each change point in the management table in the format of “time difference—change point order—anchor order”. For example, when the information stored in “change point reaching the next anchor” in the anchor table is “2 (1) -1”, the difference processing unit 15 changes the change in the form “1-2-1”. The point information is stored in the management table.

  Thereby, the difference processing unit 15 manages the arrival time of the change point when the window is shifted using the management table.

  In the anchor table of the example of FIG. 79, the total number of matches is “8 (= 3 + 3 + 2)”. The computing unit 14 performs computation by fitting the number of matches P (P = 8) and the number of items n (n = 7) to the above-described formula (A) to obtain a similarity t “t = −0.23”. .

  As described above, when the window of one time-series data is fixed and the window of the other time-series data is shifted among the two time-series data to be subjected to the similarity calculation, the number of matches is different for each anchor type. A weight is assigned to the change amount and the difference between the change amounts.

  For example, “B1 ++” of the time difference “1” indicates that the magnitude relationship does not coincide with the change point “1-” of the data 2 corresponding to the anchor “B1 +”. Therefore, “B1 + ×” is type B and the weight relationship is zero to indicate that the magnitude relationship is inconsistent.

  In addition, “C5- ◯” with a time difference “1” indicates that the magnitude relationship is coincident with the change point “3-” corresponding to the anchor “C5-”. Therefore, “C5- ◯” is type C, and the weight is “−1” to indicate that the magnitude relationship is the same.

  The difference processing unit 15 weights the anchor data for each time difference and sums the weights of all anchors. In the example of FIG. 80, the total weight is “−2”. The sum of these weights becomes the amount of change in the number of matches.

  As described above, the number of matches in the magnitude relationship before the window is shifted is “8”. The difference processing unit 15 adds the amount of change in the number of matches to the number of matches in the magnitude relationship before the window is shifted. As a result, the number of coincidence P in the magnitude relation after the window is shifted (after update) is “P = 8 + (− 2) = 6”.

  The computing unit 14 performs computation by fitting the number of matches P (P = 6) and the number of items n (n = 7) to the above-described formula (A) to obtain the similarity t “t = −0.42”. .

  FIG. 81 shows an example when the window of data 2 is shifted. Since the window is shifted, the difference processing unit 15 increases the offset of the data 2 by one. Due to the shifting of the window, the arrival time of the management table is shifted.

  For example, the change point “2+” of the data 2 reaches the anchor because the window is shifted. The change point “2+” is managed as “1-2-1” in the management table.

  Since “1-2-1” has reached zero arrival time in the management table, the difference processing unit 15 reverses the matching of the magnitude relationship of the anchor “B1-” corresponding to “1-2-1”. As a result, the anchor “B1−” at the time difference “1” is inverted to “◯”.

  The difference processing unit 15 reduces the change in the number of matches by one because the magnitude relationship of the anchor “B1-” is inverted from “×” to “◯”.

  Further, since the next change point “3-” of the data change point “2+” exists between the anchor “B1 +” and the anchor “C5-”, the difference processing unit 15 relates to the change point “3-”. Add information to the management table. The change point “3-” of data 2 is managed as “1-3-1” in the management table.

  In the example of FIG. 82, “1-4-3” of zero arrival time in the management table indicates the change point “8+” of data 2 as described above. This change point “8+” corresponds to the anchor “A7 +”.

  Therefore, the difference processing unit 15 reverses the magnitude relationship of the anchor “A7 +” to “◯”. The difference processing unit 15 decreases the amount of change in the number of matches by one because the magnitude relationship of the anchor “A7 +” is inverted from “×” to “◯”.

  The change point “8+” of data 2 reaches the anchor “C5−” when the window is shifted twice. The order indicating the anchor “C5-” is “2”. Therefore, the difference processing unit 15 stores “1-4-3” in the management table indicating the change point “8+” of the data 2 as “1-4-2” and stores it in the arrival time “2”.

  Also, the difference processing unit 15 adds “1-5-3” indicating the change point “9-” of the data 2 to the management table.

  FIG. 83 shows an example in which the difference processing unit 15 has processed all time differences. The difference processing unit 15 performs a process for obtaining a difference in the amount of change for all anchors of the data 1 based on the weighting for each type to obtain “−2”.

  Since the amount of change in the number of matches before the window is shifted is “−2”, the amount of change in the number of matches is “−4 (= (− 2) + (− 2))”. Since the number of matches in the magnitude relationship before the window is shifted is “6”, the number of matches P after the window is shifted is “P = 6−4 = 2”.

  The computing unit 14 performs computation by fitting the number of matches P (P = 2) and the number of items n (n = 7) to the above-described formula (A) to obtain the similarity t “t = −0.80”. .

  Further, the difference processing unit 15 deletes the information of the change point with zero arrival time, performs the above-described processing, and updates the management table.

  FIG. 84 shows an example when the window is shifted next. The difference processing unit 15 performs weighting for each type based on the anchor data, and obtains a difference “5” in the amount of change. Since the amount of change in the number of matches before the window is shifted is “−4”, the difference processing unit 15 adds “5” to “−4” to obtain the amount of change in the number of matches “1”.

  Since the number of matches before the window is shifted was “2”, the difference processing unit 15 adds the amount of change “1” to the number of matches to obtain the number of matches P (P = 3). The computing unit 14 performs computation by fitting the number of matches P (P = 3) and the number of items n (n = 7) to the above-described formula (A) to obtain the similarity t “t = −0.71”. .

  As shown in the example of FIG. 84, the period of the data 2 is from time “1” to “10”. Since the window has moved to the end of the period of data 2, the processing of specific example 3 ends.

<Example of number of matches using other values>
Next, an example of the number of coincidence in magnitude relation between two time series data using values different from the above examples will be described. As shown in the change point table of the example of FIG. 85, the offset and change point values are different from the above-described examples. “D1” is data 1 and “D2” is data 2.

  In the example of FIG. 85, the period of the two time-series data is from time “1” to “20”. Therefore, the period of data 1 and data 2 is “20”. FIG. 85 shows an example when the time difference is “4”. In this case, the window range is “1” to “16”.

  As shown in the example of FIG. 86, the counting unit 13 obtains the position after offset correction of the start point of data 1 in the change point table. The position after offset correction is the index described above. In the case of the example in FIG. 86, the position after offset correction is “−3 = 4-7”.

  Since the position after offset correction is “−”, the change point “4+” of data 1 is not in the window. Accordingly, at this time, the counting unit 13 does not add the number of matches, and therefore the number of matches is zero.

  The counting unit 13 moves the comparison target in order from the changing point where the offset value is small. As shown in the example of FIG. 87, the offset of the change point “19−” of data 1 is “12”, and the offset of the change point “8−” of data 2 is “6”.

  Accordingly, the counting unit 13 obtains the number of coincidence of magnitude relations by using the change point “4+” of data 1 and the change point “8−” of data 2 as a comparison target. The magnitude relationship after the position “−3” after offset correction in data 1 is “+”. Further, the magnitude relationship after the position “6” after offset correction in the data 2 is “−”, and the magnitude relationship before “5” is “+”.

  Therefore, the magnitude relationship in the range from the position “1” to “5” after offset correction is “+”, which matches. The counting unit 13 counts the number of matching magnitude relationships. Therefore, the number of matches is “5”.

  As shown in the example of FIG. 88, the change point with the smallest value after the offset correction is “19−”. In the data 1, the magnitude relationship before the position after offset correction with respect to the window range is “+” is “+”. In the data 2, the magnitude relationship between the positions after offset correction from “7” to “11” is “−”.

  Therefore, the data 1 and the data 2 in the positions after the offset correction from “7” to “11” are inconsistent. On the other hand, the magnitude relation of data 1 becomes “+” after the position “12” after the offset correction.

  For this reason, the magnitude relationship between data 1 and data 2 coincides at position “12” after offset correction. The counter 13 counts the number of matches and obtains the number of matches “1”. The total number of matches so far is “6 = 1 + 5”.

  As shown in the example of FIG. 89, the next change point with the smallest value after offset correction is “22+” of data 1. In data 1, the magnitude relationship between the positions “13” to “14” after offset correction is “−”, and the magnitude relationship after “15” is “+”.

  In the data 2, the magnitude relationship after the position “6” after the offset correction is “−”. Therefore, data 1 and data 2 have the same magnitude relationship at positions “13” to “14” after offset correction. Accordingly, the counting unit 13 counts the number of matches and obtains the number of matches “2”. The total number of matches so far is “8 = 6 + 2”.

  As shown in the example of FIG. 90, the next change point with the smallest value after offset correction is “23+” of data 2. In the data 1, the magnitude relationship after the position “15” after the offset correction is “+”.

  In the data 2, the magnitude relationship from the position “6” to “20” after the offset correction is “−”. Since the window range is “1” to “16”, the comparison target in this case is the position “15” to “16” after offset correction.

  The magnitude relationship between positions “15” to “16” after offset correction of data 1 is “+”, and the magnitude relation between positions “15” to “16” after offset correction of data 2 is “−”. Therefore, the magnitude relationship between data 1 and data 2 in this range does not match.

  Therefore, the number of matches counted by the counting unit 13 is zero. The total number of matches so far is “8 = 8 + 0”.

  As described above, the counting unit 13 counts the number of matches between the data 1 and the data 2 in the window range “1” to “16”.

<An example of a flowchart showing the flow of processing of the embodiment>
Next, a flowchart showing a processing flow of the embodiment will be described. As shown in the example of FIG. 91, the data processing apparatus 1 determines time-series data that is a target of similarity calculation and a window (period) that is a comparison target among the time-series data (step S1). Hereinafter, the time series data may be referred to as a series.

  In the embodiment, the detection unit 12 reads target time-series data from the storage unit 11. At least two pieces of time series data are read from the storage unit 11. The detection unit 12 detects a change point within the window range for all time series data to be processed (step S2). Hereinafter, the process of detecting the change point is referred to as process A.

  When the calculation unit 14 calculates the similarity for all target time-series data (no in step S3), the process ends.

  The difference processing unit 15 determines whether both windows set in the two time-series data to be compared are fixed, both windows are shifted, or one window is shifted (step S4). .

  The difference processing unit 15 performs the determination in step S4 based on whether either of the windows can be shifted, one of the windows can be shifted, or both of the windows cannot be shifted. May be.

  When both windows are fixed, the similarity is calculated based on the detected change point without shifting the windows (step S5). The process of step S5 is the process of specific example 1 described above (hereinafter referred to as process B).

  When both windows are shifted, the difference processing unit 15 performs difference processing while shifting both windows, and the calculation unit 14 calculates the similarity (step S6). The process of step S6 is the process of specific example 2 described above (hereinafter referred to as process C).

  When one of the windows is shifted, the difference processing unit 15 performs difference processing while shifting one of the windows, and the similarity is calculated by the calculation unit 14 (step S7). The process of step S7 is the process of specific example 3 described above (hereinafter referred to as process D).

  Process A (process for detecting a change point) will be described with reference to the flowchart of FIG. The detection unit 12 determines whether there is time-series data that has not been subjected to the process of detecting the change point among the target time-series data (step S11).

  If the process of detecting the change point has been completed for all time series data (no in step S11), the process ends. When there is time-series data that has not been subjected to the process of detecting the change point (yes in step S11), the detection unit 12 acquires the time-series data from the storage unit 11 and obtains the period of the time-series data ( Step S12).

  The detection unit 12 detects a monotone section (monotonically increasing section and monotonically decreasing section) in the acquired time series data (step S13). The detection unit 12 assigns “1” to the variable i (i is an integer). The variable i indicates a time difference.

  The detection unit 12 determines whether the variable i is less than the time series data period (step S15). When the variable i is equal to or longer than the time series data period (no in step S15), the process returns to step S11.

  When the variable i is less than the time series data period (yes in step S15), the detection unit 12 determines the above-described block based on the monotonic section and the variable i (step S16). Then, the detection unit 12 detects the first change point value (initial value) (step S17).

  The detection unit 12 determines whether there is an unprocessed block (step S18). When there is an unprocessed block (yes in step S18), it is determined whether the block is included in the same monotone section (step S19).

  When the block is not included in the same monotone section (no in step S19), the detection unit 12 determines whether the block is “a block in which a range of values is separated” (step S20).

  When the block is not a “block whose value range is separated” (no in step S20), the block is a block for which a change point is to be detected. In this case, the detection unit 12 determines whether the block length is long (step S21).

  The length of the block is a range of time series data. Whether or not the length of the block is long may be arbitrarily set. For example, a threshold value may be set for the block length, and when the block length exceeds the threshold value, it may be determined that the block length is long.

  When it is determined that the length of the block is long (yes in step S21), the detection unit 12 divides the block as described above (step S22). After the block is divided, the process returns to step S21. Therefore, one block may be divided into two blocks, or may be divided into three or more blocks.

  The detection unit 12 searches for a change point where the magnitude relationship changes within the block (the range of the time-series data) (step S23). And the detection part 12 moves the block which searches a change point to the following block (step S24). If yes in step S19 and yes in step S20, the process proceeds to step S24.

  If no in step S18, that is, if there is no unprocessed block, the detection unit 12 increments the variable i (step S25). The detection unit 12 performs the above processing until the variable i reaches the time series data period.

  Next, process B will be described with reference to the flowchart of FIG. In the case of process B, the windows of the two time series data to be compared are fixed. First, a comparison period (window range) is determined (step S31).

  The counting unit 13 substitutes zero for the variable P (P is an integer) (step S32). The variable P indicates the number of matches. The counting unit 13 substitutes “1” for the variable i (step S33).

  The counting unit 13 determines whether the variable i is less than the time series data period (step S34). When the variable i is less than the time series data period (yes in step S34), the detection unit 12 selects change point data of the time difference of the variable i (step S35).

  The counting unit 13 performs the process of the first specific example described above, obtains the number of matches within the window range of the time-series data for each change point of the change point data, and adds the number of matches to the variable P (step S36). .

  The counting unit 13 increments the variable i (step S37), and the process returns to step S34. The processes in steps S35 to S37 are performed until the variable i indicating the time difference reaches the time series data period.

  When the variable i has reached the time series data period (no in step S34), the counting unit 13 adds up the number of matches to obtain the number of matches P. The calculation unit 14 performs calculation by applying the number of matches P and the number of items to the above-described formula (A), and obtains the similarity between the time series data (step S38). Thereafter, the process B ends.

  Next, the process C will be described with reference to the flowchart of FIG. First, a comparison period (window range) is determined (step S41). The counting unit 13 performs the above-described processing of the first specific example, and obtains a matching number P of magnitude relations within the range of the initially set window (step S42).

  The difference processing unit 15 uses the number of matches at the front end and the rear end of the window to obtain the amount of change d of the number of matches described in the specific example 2 (step S43). The computing unit 14 performs computation by applying the number of matches P and the number of items to the above-described equation (A) to obtain a similarity (step S44).

  The difference processing unit 15 determines whether there is a next time at which the window can be shifted (step S45). If there is a next time at which the window can be shifted (Yes in step S45), the difference processing unit 15 shifts the windows respectively set for the two time-series data to be compared (step S46).

  The difference processing unit 15 performs the processing of the specific example 2 described above, and updates the amount of change d of the number of matches based on the changing points entering and exiting the window (step S47). The difference processing unit 15 adds the amount of change d of the number of matches to the number of matches P obtained before the window is shifted (step S48).

  Thereby, the coincidence number P of the magnitude relation after the window is shifted is obtained. In step S44, the calculation unit 14 performs calculation by fitting the number of matches P after the window is shifted and the number of items in the window range to the above-described equation (A), and obtains the similarity.

  In step S45, it is determined whether there is a next time when the window can be shifted. When it is determined that there is no next time at which the window can be shifted (No in step S45), the process C ends.

  Next, process D will be described with reference to the flowchart of FIG. First, a comparison period (window range) is determined (step S51). The counting unit 13 performs the process of the specific example 1 described above, and obtains a matching number P of magnitude relations within the range of the initially set window (step S52).

  The difference processing unit 15 obtains a change amount d of the number of matches using the fixed time-series data (sequence change points not shifted) and the number of matches at the anchors at the front and rear ends of the window (step S53).

  The calculation unit 14 applies the number of matches P and the number of items in the window range to the above-described formula (A) to obtain the similarity between the two time-series data (step S54).

  The difference processing unit 15 determines whether there is a next time at which the non-fixed window can be shifted (step S55). If there is a next time at which the window can be shifted (Yes in step S55), the difference processing unit 15 shifts the window that is not fixed (step S56).

  The difference processing unit 15 performs the process of the specific example 3 described above, and adds the amount of change d of the number of matches to the number of matches P obtained before the window is shifted (step S57). Thereby, the coincidence number P of the magnitude relation after the window is shifted is obtained.

  The calculation unit 14 applies the number of matches P and the number of items in the window range after the window is shifted to the above-described formula (A) to obtain the similarity between the two time-series data (step S58).

  The difference processing unit 15 updates the change amount d of the number of matches from the change point that has reached the anchor described above (step S59). If there is no next time at which the window can be shifted in step S55 (no in step S55), the process D ends.

<Others>
FIG. 96 shows an example of three types of time series data (data A, data B, and data C). Data A is time-series data with a slow local change and a large locality. Since time series data such as data A has few change points, the time for obtaining the number of coincidence of magnitude relations is shortened, and the time for calculating the degree of similarity between the time series data is also shortened.

  The data B is data sampled at a fine cycle, and the value of the time series data changes from a small value to a large value as a whole waveform. Since such time-series data also has a certain degree of locality, the time for obtaining the number of coincidence of magnitude relations is shortened, and the time for calculating the similarity between the time-series data is also shortened.

  Data C is time-series data with large fluctuations in value. Since time series data such as data C has a small locality and a large number of change points, the time for obtaining the number of coincidences of magnitude relationship is longer than that of data A and data B.

  Therefore, in the case of data C, the time for calculating the degree of similarity between time series data is longer than that of data A and data B. However, even in the case of data C, the number of coincidence of magnitude relation is obtained based on the change point, and the degree of similarity is calculated based on the number of coincidence, so that the time for calculating the degree of similarity is shortened.

  The present embodiment is not limited to the above-described embodiment, and various configurations or embodiments can be taken without departing from the gist of the present embodiment.

DESCRIPTION OF SYMBOLS 1 Data processor 11 Memory | storage part 12 Detection part 13 Counting part 14 Calculation part 15 Difference processing part 111 Processor 112 RAM
113 ROM

Claims (8)

For each of the two time-series data to be compared, a detection unit that detects a time at which the tendency of an increase or decrease in value with respect to time changes as a change point;
The two time is set separately for each of the series data, within a predetermined period including a plurality of identical period width, the two time-series data, said predetermined time period for the plurality of same period width respectively When the same order from the first time is sequentially compared, the number of matches in which the change in tendency at the corresponding time in the same order matches is counted from the detection time of the change point for the two time-series data. A counting unit;
An arithmetic unit that calculates the similarity between the two time-series data based on the number of matches ;
A data processing apparatus comprising: The detection unit is configured to determine a magnitude relationship with respect to a time value at a later time having a predetermined time difference from the time of each time value included in each of the two time series data. As the information representing the trend, when the detected magnitude relations are arranged in order of time while being detected for each time difference, the time when the magnitude relation changes with the passage of time is used as the change point for each time difference. To detect
The counting unit counts the number of matches for each of the time differences,
The computing unit computes the similarity based on the number of matches for each time difference.
The data processing apparatus according to claim 1. Shifting the predetermined period set for the two time series data on the time axis, a difference processing unit for determining the number of matches of variation which changes in the predetermined time period is shifted, further comprising a
The counting unit shifts the predetermined period based on the number of matches counted by the counting unit before the predetermined time is shifted and the amount of change in the number of matches obtained by the difference processing unit. match the number of the sought after,
The calculation unit calculates the similarity based further on the number of matches after the predetermined period is shifted.
The data processing apparatus according to claim 2. In the case where the predetermined period is shifted in the same direction on the time axis by the same time for both of the two time series data , the difference processing unit determines the predetermined period from the change points as the time. It will be included in the predetermined time period when shifted 1 time min on the axis, or selecting the change point as a departing from the predetermined time period, by inverting the size relation of the selected change points and arising when the variation in the number of changes in a change in the tendency matches for the selected change points, determined as the number of matches variation at the time of shifting the 1 time amount,
The data processing apparatus according to claim 3. The difference processing unit is a table showing a positional relationship on the time axis between the predetermined period and the change point based on the two time series data and the change point data indicating the change point for each time difference. to manage,
The data processing apparatus according to claim 3 or 4, characterized in that The two time of the series data, said for one of the time-series data given period is shifted, when the other of the time series data is the predetermined time period is not shifted, the differential processing unit,
For the time series data of the other, each with the front end is the first time, said assimilation each of the rear end is the first time is the changing point within said predetermined period time difference subsequent to the predetermined time period To
Regarding the time determined to be not the change point at each of the front end and the rear end, the time is newly set as the change point, and the time that is the newly set change point is detected. Reverse the magnitude relationship,
As well as processing
Whether the magnitude relationship for the time that is the change point in the other time series data after the processing matches the magnitude relationship for the corresponding time in the one time series data before being shifted For each time difference, the change point that is the front end, the change point that is the rear end, and a change point that is not the rear end of the time within the predetermined period,
For the change point that is the front end, a weight “0” is given to the change point when it is determined that the magnitude relationship matches, and a weight “+1” is assigned to the change point when the magnitude relationship does not match. To the change point,
For the change point that is the rear end, a weight “−1” is given to the change point when it is determined that the magnitude relationship matches, and a weight “0” when it is determined that the magnitude relationship does not match. Is given to the change point,
For a change point that is not the rear end of the time within the predetermined period, when it is determined that the magnitude relationship matches, a weight “−1” is given to the change point, and it is determined that the magnitude relationship does not match. If this is the case, give the weight “+1” to the change point,
A value obtained by summing the weights given to each change point is obtained as a change amount of the number of coincidence when the predetermined period is shifted by one time on the time axis with respect to the one time series data.
The data processing apparatus according to claim 3. Computer
For each of the two time-series data to be compared, the time at which the tendency of increase or decrease in value over time changes is detected as a change point,
The two time is set separately for each of the series data, within a predetermined period including a plurality of identical period width, the two time-series data, said predetermined time period for the plurality of same period width respectively When the same order from the first time in the order is sequentially compared, the number of matches in which the change in tendency at the corresponding time in the same order matches is counted from the detection time of the change point for the two time series data. ,
Calculating a similarity between the two time-series data based on the number of matches ;
A data processing method. On the computer,
For each of the two time-series data to be compared, the time at which the tendency of increase or decrease in value over time changes is detected as a change point,
The two time is set separately for each of the series data, within a predetermined period including a plurality of identical period width, the two time-series data, said predetermined time period for the plurality of same period width respectively When the same order from the first time in the order is sequentially compared, the number of matches in which the change in tendency at the corresponding time in the same order matches is counted from the detection time of the change point for the two time series data. ,
Calculating a similarity between the two time-series data based on the number of matches ;
A data processing program for executing a process.