JP7067748B2 - Time-series data evaluation device and time-series data evaluation program - Google Patents

Description

The present invention relates to a time-series data evaluation device and a time-series data evaluation program.

For example, an index called the Lyapunov exponent is often used as a quantification method for grasping the degree of chaos in time series data. When calculating the Lyapunov exponent, it is necessary to know the information of the data generation source (discrete system difference equation, continuous system differential equation, etc.). When the information of the data generation source is unknown, a means of estimating from a large amount of data is given, but the process related to the so-called "estimation of the embedded dimension" repeats adjustment while observing the state of the system for each dimension. Despite the necessity and complexity, there is a problem that the Lyapunov exponent cannot always be uniquely obtained (Non-Patent Documents 5, 6 and 7).

In recent years, an index called "Chaos Degree" based on information theory has been proposed (Non-Patent Document 1). The following is an example of a calculation method for the chaos scale.

により、

として生成されているものとする。 <Definition of chaos scale>
Time-series data with data length n + 1
{Ξ ₀ , ξ ₁ , ξ ₂ , ..., ξ _n } ... (1)
It is expressed as.
The data is the difference equation τ

By

It is assumed that it is generated as.

The interval I≡ [a, b] containing the above ξ _k is equally divided into m intervals. Assuming that this division interval is X _i (i = 1, 2, ..., M), the following equation (2) holds for I.

上記において＃｛（条件式）｝は、（条件式）を満たす数を意味する。 Here, the probability distribution p (i) such that ξ _k ∈ X _i and the joint probability distribution p (i, j) such that ξ _k ∈ X _i and ξ _{k + 1} ∈ X _j are given by the following equation (3). Calculate as in (4).

In the above, # {(conditional expression)} means a number that satisfies (conditional expression).

ただし、０ｌｏｇ０＝０とする。 When the probability distribution p (i) and the joint probability distribution p (i, j) are obtained as described above, the chaos scale H is defined as the following equation (5) or equation (6).

However, 0log0 = 0.

カオス尺度Ｈの値は大きいほどカオス性が大きい（複雑性が高い）ことを意味する。即ち、カオス尺度Ｈに関する解釈は、次のようにまとめることができる。

The minimum value of the above chaos scale H is 0, but the maximum value is logm depending on the number of divisions m.

The larger the value of the chaos scale H, the greater the chaos (higher complexity). That is, the interpretation of the chaos scale H can be summarized as follows.

It is known that this chaos scale and the Lyapunov exponent behave very similar (Non-Patent Documents 2, 3, and 4). 1 to 3 show changes in the values of the chaos scale and the Lyapunov exponent of the logistic map (a: 3.5 to 4.0). FIG. 1 shows the number of divisions m = 80 and the number of subdivisions M = 80, FIG. 2 shows the number of divisions m = 160 and the number of subdivisions M = 160, and FIG. 3 shows the number of divisions m = 320 and subdivisions. The number M = 320 is shown. In each case, n of the data length (n + 1) is 10000000. With reference to these FIGS. 1 to 3, it is clear that the chaos scale and the Lyapunov exponent make similar changes. The chaos scale has a feature that it can be uniquely calculated only from data.

In recent years, the inventors of the present application have clarified the mathematical relationship between the chaos scale and the Lyapunov exponent (Non-Patent Documents 8, 9, 10, 11).

の関係にあることを示した（非特許文献９、１１）。上記式（７）において、Ｄ関数と称するＤ（ｘ）に相当する部分を小さく抑えることによりカオス尺度をリアプノフ指数に近接させる手法を基本とした構成を有する時系列データ解析装置及び時系列データ解析用プログラムの発明を出願した（特願２０１９－１９００５４）。この発明は、修正カオス尺度と称する指数を求めるものとして説明した。 Further, the inventors of the present application express the division of the chaos scale as Δx≡ || Xi || (j = 1, 2, ..., M), and the chaos scale is in the limit of Δx → 0.

(Non-Patent Documents 9 and 11). In the above equation (7), a time-series data analysis device and time-series data analysis having a configuration based on a method of bringing the chaos scale closer to the Lyapunov exponent by keeping the portion corresponding to D (x) called the D function small. An application was filed for the invention of the program (Japanese Patent Application No. 2019-190054). The present invention has been described as finding an exponent called the modified chaos scale.

Furthermore, the inventors of the present application have filed an invention of a time-series data analysis device and a time-series data analysis program for obtaining an index called an extended chaos scale, which is an improved chaos scale (Japanese Patent Application No. 2019-190055). The extended chaos scale will be described below.

<Extended Chaos Scale>
Time-series data having a data length of n + 1 is represented by the equation (8).
{Ξ ₀ , ξ ₁ , ξ ₂ , ..., ξ _n } ... (8)
As described in <Definition of chaos scale>, if the division interval X _i for the partition number m is X _i (i = 1, 2, ..., M), the following equation (9) holds for I. Met. The equation (9) and the equation (2) are the same.

ここで、ξ_k∈Ｘ_iとなる確率分布ｐ（ｉ）と、ξ_k∈Ｘ_i，ξ_k+1∈Ｘ´_jとなる同時確率分布ｐ´（ｉ，ｊ）は、次に示す式（１１）と式（１２）のようになる。

Assuming that X'i is _X'i ( _i = 1, 2, ..., M × M) for the subdivided section obtained by dividing the above divided section into M for each divided section, the following equation (10) is obtained for I. It holds.

Here, the probability distribution p (i) such that ξ _k ∈ X _i and the joint probability distribution p'(i, j) such that ξ _k ∈ X _i and ξ _{k + 1} ∈ _X'j are expressed by the following equations. It becomes like (11) and equation (12).

The probability distribution calculation means obtains the probability distribution p (i) by the above equation (11). Further, the joint probability calculation means obtains the joint probability p'(i, j) by the above equation (12).

Further, in the present embodiment, the extended chaos scale H ^* is calculated by the extended chaos scale calculating means, and h represented by the following equations (13) and (14) as intermediate values for obtaining the extended chaos scale H ^* . Is calculated by the extended chaos scale calculation means.

ただし、
０ｌｏｇ０＝０
である。 In order for the extended chaos scale calculation means to calculate the extended chaos scale H ^* , the following equation (15) is used. That is, the extended chaos scale calculating means calculates the extended chaos scale H ^* by using the following formula (15) and either the above formula (13) or the above formula (14).

however,
0log0 = 0
Is.

Masanori Ohya, Toshihide Hara, "Basics of Mathematical Physics and Mathematical Information," Modern Science, 2016 K.Inoue, M.0hya, K.Sato, "Application of chaos degree to some dynamical systems," Chaos, Solitons & Fractals, Volume 11, Issue9, July2000, Pages 1377-1385 K.Inoue, "Basic properties of entropic chaos degree in classical systems," Internationa1 journal on information 16 (12 (B)), December 2013, 8589-8596 Satoshi Inoue, "Handling of Semi-Periodic Orbits in the Chaos Scale," Journal of the Japan Society for Industrial and Applied Mathematics, VOL. 25, No2, 2005. Year, pp. 105-115 Daiki Okada, Ken Umeno, "New Nonlinear Time Series Analysis Method-Chaos Analysis by Moving Maximum Lyapunov Exponent Line-," Laser Society of Japan, Vol. 43, No6 (2015) 1993, pp. 117-134. A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastano, "Determining Lyapunov Exponents from a Time Series," Physica D, Vol. 16, No3,1985, pp285-317. M. T. Rosenstein, J. J. Collins and C. J. De Luca, "A Practical Method for Calculating Largest Lyapunov Exponents for Small Data Sets," Physica D, Vol.65,1993, pp.117-134. Hidetoshi Kadomi, Tomoyuki Manao, "On the Mathematical Relationship between the Chaos Scale and the Ryapunov Index," Institute of Electronics, Information and Communication Engineers, 2017 3rd CCS Study Group (2), November, 2017 Hidetoshi Okutomi, Tomoyuki Manao, "Calculation of the limit value of the chaos scale" Japan Society for Industrial and Applied Mathematics 2018 Annual Meeting, Applied Chaos (1) -3, September 2018 Tomoyuki Mao, Hidetoshi Kudomi, Ken Umeno, "Calculation Method of Chaos Scale", Japan Society for Industrial and Applied Mathematics, 2018 Annual Meeting, Applied Chaos (1) -4, September 2018 Hidetoshi Kudomi, "Consideration on the Relationship between Chaos Scale and KS Entropy," Institute of Electronics, Information and Communication Engineers, 2018 1st CCS Study Group (2), June, 2018 Tomoyuki Mao, Hidetoshi Katotomi, "On the Relationship between the Chaos Scale of Heart Rate Interval Data and Autonomic Nervous Activity," Japan Society for Industrial and Applied Mathematics 2016 Annual Meeting, Applied Chaos (2) -1, September 2016 Tomoyuki Mao, Hidetoshi Okutomi, "On the relationship between the chaos of heart rate variability and parasympathetic nerve activity", Institute of Electronics, Information and Communication Engineers, 3rd CCS Study Group (1), November, 2017

An object of the present invention is to provide a time-series data evaluation device and a time-series data evaluation program capable of performing time-series data evaluation with high accuracy regardless of the size of the number of divisions m or the number of subdivisions M. ..

In the time-series data evaluation device according to the embodiment of the present invention, the time-series data {ξ ₀ , ξ ₂ , ξ ₃ , ..., ξ _n } with the data length n + 1 is the map τ, where n is a positive integer. When ξ _k = τ (ξ _k-1 ) = τ ^k (ξ ₀ ), k = 1, 2, ..., N, the interval I containing ξ _k is equal to m intervals. For the divided division section X _i (i = 1, 2, ..., M), the external measure and the simultaneous external measure are obtained and the inner measure is obtained for the data having the subdivision section X _j in which each division section is further divided into M equal parts. An external measure / internal measure calculation method for obtaining a measure and an internal measure at the same time,
Based on the external measure and the simultaneous external measure, the constant density simultaneous external measure when the data density is constant and the i-fixed external measure total frequency are obtained, and the data density is calculated based on the internal measure and the simultaneous internal measure. A constant density information calculation means for obtaining a constant density simultaneous internal measure and i-fixed internal measure total frequency when the value is constant.
Based on the constant density simultaneous external measure and the i-fixed external measure total frequency, the external measure probability distribution related to the external measure and the external measure conditional probability distribution when the data density is constant are obtained, and the constant density simultaneous internal measure is obtained. And the probability distribution calculation means for obtaining the internal measure conditional probability distribution when the internal measure probability distribution and the data density are constant for the internal measure based on the i-fixed internal measure total frequency.
The external measure data evaluation value related to the external measure is obtained based on the external measure probability distribution and the external measure conditional probability distribution, and the internal measure data evaluation value related to the internal measure based on the internal measure probability distribution and the internal measure conditional probability distribution. External measure / inner measure evaluation value calculation means to obtain
It is characterized by comprising a time-series data evaluation value calculation means for calculating the evaluation value of the entire time-series data based on the outer measure data evaluation value and the inner measure data evaluation value.

Changes in the chaos scale of the logistic map (a: 3.5 to 4.0), the Lyapunov exponent, and the evaluation value calculated in the embodiment of the present invention when the number of divisions m = 80 and the number of subdivisions M = 80. The figure which shows. Changes in the chaos scale of the logistic map (a: 3.5 to 4.0), the Lyapunov exponent, and the evaluation value calculated in the embodiment of the present invention when the number of divisions m = 160 and the number of subdivisions M = 160. The figure which shows. Changes in the chaos scale of the logistic map (a: 3.5 to 4.0), the Lyapunov exponent, and the evaluation value calculated in the embodiment of the present invention when the number of divisions m = 320 and the number of subdivisions M = 320. The figure which shows. The block diagram of the time series data evaluation apparatus which concerns on embodiment of this invention. The functional block diagram of the time series data evaluation apparatus which concerns on embodiment of this invention. The flowchart which shows the operation when the CPU 101 performs the calculation and obtains the inner measure c ₃ [i] and the simultaneous inner measure c ₄ [i] [j]. The extended chaos scale of the logistic map (a: 3.5 to 4.0), the Lyapunov exponent, and the evaluation value calculated in the embodiment of the present invention when the number of divisions is m = 80 and the number of subdivisions is M = 80. The figure which shows the change. The extended chaos scale of the logistic map (a: 3.5 to 4.0), the Lyapunov exponent, and the evaluation value calculated in the embodiment of the present invention when the number of divisions is m = 160 and the number of subdivisions is M = 160. The figure which shows the change. The extended chaos scale of the logistic map (a: 3.5 to 4.0), the Lyapunov exponent, and the evaluation value calculated in the embodiment of the present invention when the number of divisions is m = 320 and the number of subdivisions is M = 320. The figure which shows the change.

Hereinafter, the time-series data evaluation device and the time-series data evaluation program according to the embodiment of the present invention will be described with reference to the accompanying drawings. In each figure, the same components are designated by the same reference numerals, and duplicate description will be omitted. FIG. 4 shows a block diagram of the time series data evaluation device 100 according to the embodiment. The time-series data evaluation device 100 can be configured by a cloud computer, a server computer, a personal computer, or another computer.

In the time-series data evaluation device 100, the CPU 101 performs operations based on the programs and data of the main memory 102. An external storage device 104 is connected to the CPU 101 via a bus 103, and a time-series data evaluation program is stored in the external storage device 104. The CPU 101 reads a time-series data evaluation program from the external storage device 104 to the main memory 102 and executes this program to function as a time-series data evaluation device.

A time-series data supply unit 105 is connected to the bus 103 in addition to the external storage device 104. The time-series data supply unit 105 can capture and hold time-series data in real time from an external sensor or the like, or capture and hold time-series data collected by some external device or the like. Can be done. Further, the device may be capable of holding and supplying the time-series data by setting a medium for storing the collected time-series data. Further, it may have all the above configurations. In any case, when the CPU 101 executes a time-series data evaluation program to evaluate the time-series data, the time-series data is supplied from the time-series data supply unit 105.

The result output unit 106 is connected to the bus 103. The result output unit 106 can be a device such as a display device or a printer that outputs the result processed by the time series data evaluation device 100. Further, the result output unit 106 may be a medium for storing the result processed by the time-series data evaluation device 100, and is a device for transmitting the processing result to the processing requester (client) via a line or the like. Is also good.

By executing the time-series data evaluation program stored in the external storage device 104, each means shown in FIG. 5 is realized. That is, as shown in FIG. 5, the time-series data evaluation device 100 includes an outer measure / inner measure calculation means 201, a constant density information calculation means 202, a probability distribution calculation means 203, and an outer measure / inner measure evaluation value calculation means 204. , The time-series data evaluation value calculation means 205 is provided.

The time-series data evaluation device 100 of the present embodiment obtains the <evaluation value> shown below, suppresses the difference between the evaluation value obtained by this and the Lyapunov exponent, and uses the evaluation value as the estimated value of the Lyapunov exponent. It works. This evaluation value can also function as an estimated value of KS entropy.

In the external measure / inner measure calculation means 201, the time series data {ξ ₀ , ξ ₂ , ξ ₃ , ..., ξ _n } with the data length n + 1 is ξ _k = by the mapping τ, where n is a positive integer. When τ (ξ _k-1 ) = τ ^k (ξ ₀ ), k = 1, 2, ..., N, the section I containing ξ _k is equally divided into m sections. For X _i (i = 1, 2, ..., M), for the data having the subdivided section X _j in which each divided section is further divided into M equal parts, the outer measure and the simultaneous external measure are obtained, and the inner measure and the inner measure are simultaneously included. It asks for a measure.

Specifically, for time-series data {ξ ₀ , ξ ₂ , ξ ₃ , ..., ξ _n } with a length of n + 1, the outer measure counter c ₁ [i] and the simultaneous outer measure counter c ₂ [ The CPU 101 calculates the values of i] and [j] by the following equations (16) and (17) to obtain an outer measure c ₁ [i] and a simultaneous outer measure c ₂ [i] [j].

The CPU 101 calculates the values of the inner measure counter _{c 3} [i] and the simultaneous inner measure counter c ₄ [i] [j] by the algorithm of the flowchart shown in FIG. Obtain the measure c ₄ [i] [j]. The operation will be described with reference to the flowchart of FIG.

The CPU 101 performs the process shown in the flowchart of FIG. That is, in steps S11 to S25, i is stepped from 1 to m one by one to perform processing. In step S11, i is stepped to 1, and the values of the simultaneous external measure counter c ₂ [i] [1] are set in the simultaneous internal measure counter c ₄ [i] [1] (S12), and the simultaneous internal measure counter is set. c ₄ [i] [m × M] is set to the value of the simultaneous outer measure counter c ₂ [i] [m × M] (S13). Next, the process proceeds to step S14.

In steps S14 to S20, j is stepped from 2 to m × M-1 one by one to perform processing. Therefore, in step S15, it is detected whether the value of the simultaneous outer measure counter c ₂ [i] [j + 1] is larger than 0 and the value of the simultaneous outer measure counter c ₂ [i] [j-1] is larger than 0. If YES, the value of the simultaneous external measure counter c ₂ [i] [j] is set in the simultaneous internal measure counter c ₄ [i] [j] (S16). When NO is set in step S15, 0 is set in the simultaneous internal measure counters c ₄ [i] and [j] (S18). In step S20, it is detected whether j is m × M-1 (S20), and if NO, the process returns to step S14 to advance j, and steps S15 to S20 are repeated.

If YES in step S20, 0 is set in the inner measure counter c ₃ [i] (S21), and j is stepped from 1 to m × M one by one to proceed from step S22 to step S24. .. In the process from step S22 to step S24, the value of the inner measure counter c ₃ [i] obtained by stepping j from 1 to m × M to the inner measure counter c ₃ [i] and the simultaneous inner measure counter c. ₄ When the sum with the values of [i] and [j] is set and j = m × M, unless i is m, the process returns to step S11 and steps i to 1, and the processing after step S12. Continue.
As described above, the inner measure c ₃ [i] and the simultaneous inner measure c ₄ [i] [j] can be obtained.

Next, the CPU 101 operates as the constant density information calculation means 202. Based on the external measure and the simultaneous external measure, the constant density information calculation means 202 obtains the constant density simultaneous external measure and the i-fixed external measure total frequency when the data density is constant, and simultaneously obtains the inner measure and the simultaneous external measure. Based on the inner measure, the constant density simultaneous internal measure when the data density is constant and the i-fixed internal measure total frequency are obtained. Before performing this process, the total frequency n for the outer measure and the total frequency n ^* for the inner measure are obtained by the following equations (18) and (19).

一方、内測度に関する全度数ｎ^*は次の通り、一般的には、外測度に関する全度数ｎよりも小さな値となることに留意する。

The total measure with respect to the outer measure is a total value equal to the number of data n as follows.

On the other hand, it should be noted that the total frequency n ^* for the inner measure is generally smaller than the total frequency n for the outer measure as follows.

Next, the CPU 101 obtains a constant density simultaneous external measure d ₂ [i] [j] when the data density is constant by the equation (20), and a constant density simultaneous internal measure d ₄ when the data density is constant. [I] and [j] are obtained by the equation (21). Further, the i-fixed outer measure total frequency t ₂ [i] is obtained by the following equation (22), and the i-fixed inner measure total frequency t ₄ [i] is obtained by the following equation (23).

ｉ＝１，２，・・・，ｍに対して、

For i = 1, 2, ..., m, j = 1, 2, ..., m × M

For i = 1, 2, ..., m

Next, the CPU 101 performs processing as the probability distribution calculation means 203. That is, the probability distribution calculation means 203 uses the following equation (24) for the outer measure probability distribution p _out (i) relating to the outer measure and the outer measure conditional probability distribution _p'out (j | i) when the data density is constant. ), Equation (25), and Equation (26), the inner measure probability distribution _pinn (i) for the inner measure and the inner measure conditional probability distribution _p'inn (j | i) when the data density is constant. Is obtained by the following equations (27), (28), and (29).

Further, when the CPU 101 uses the outer measure / inner measure evaluation value calculation means 204 to obtain the outer measure data evaluation value related to the outer measure, the CPU 101 is specified by the following equations (30) and (31) prior to this. When obtaining the above-mentioned internal measure data evaluation value related to the internal measure while obtaining the measure data evaluation intermediate value h _out , prior to this, the following equations (32) and (33) are used to obtain the internal measure data evaluation intermediate value h _inn . Ask for.

Further, the CPU 101 obtains the outer measure data evaluation value H * out based on the outer measure data evaluation intermediate value h _out , and the outer measure / inner measure evaluation value calculation means 204 obtains the outer measure data evaluation value H ^* _out by the following formula (34), and evaluates the inner measure data. The inner measure data evaluation value H ^* _inn is obtained by the following equation (35) based on the intermediate value h _inn .

The CPU 101 functions as a time series data evaluation value calculation means 205. The time-series data evaluation value calculation means 205 calculates the evaluation value of the entire time-series data based on the outer measure data evaluation value H ^* _out and the inner measure data evaluation value H ^* _inn .

The CPU 101, as the time-series data evaluation value calculation means 205, calculates the evaluation value of the entire time-series data by an operation of obtaining the average of the outer measure data evaluation value and the inner measure data evaluation value. Specifically, the evaluation value H ^* of the entire time series data is calculated by obtaining the arithmetic mean as shown in the following equation (36).

The evaluation value H ^* of the entire time-series data can be a graph that matches the Lyapunov exponent with extremely high accuracy, and can be used as an estimated value of the Lyapunov exponent. 1 to 3 show changes in the chaos scale of the logistic map (a: 3.5 to 4.0) and the values of the Lyapunov exponent, as well as changes in the evaluation value H ^* of the entire time series data of the present embodiment. ing. According to FIGS. 1 to 3, it can be seen that the evaluation value H ^* of the entire time series data is in agreement with the Lyapunov exponent with extremely high accuracy.

7 to 9 show changes in the values of the extended chaos scale and the Lyapunov exponent of the logistic map (a: 3.5 to 4.0), as well as changes in the evaluation value H ^* of the entire time series data of the present embodiment. Shows. FIG. 7 shows the number of divisions m = 80 and the number of subdivisions M = 80, FIG. 8 shows the number of divisions m = 160 and the number of subdivisions M = 160, and FIG. 9 shows the number of divisions m = 320 and subdivisions. The number M = 320 is shown. In each case, n of the data length (n + 1) is 10000000. According to these FIGS. 7 to 9, it can be seen that the evaluation value H ^* of the entire time series data is in agreement with the Lyapunov exponent with extremely high accuracy even when compared with the extended chaos scale.

In addition, when calculating the evaluation value H ^* of the entire time series data, it was shown that the arithmetic mean of the outer measure data evaluation value H ^* _out and the inner measure data evaluation value H ^* _inn is obtained. Not limited to this. For example, a method of obtaining a geometric mean with the above-mentioned internal measure data evaluation value H ^* _inn can be adopted, and a weighted average “(1-p) H ^* _out + pH ^* _inn ” with p as an appropriate weight can be adopted. , Etc. may be used. Further, it may be a generalized average "[(H ^* _out ^ m + H ^* _inn ^ m) / 2] ^ (1 / m)" which is a generalization of the arithmetic mean. As a special case of the general average, setting m to 1 results in an "arithmetic mean", and setting m to -1 in the generalized average makes it a "harmonic mean".

100 Time series data evaluation device 102 Main memory 103 Bus 104 External storage device 105 Time series data supply unit 106 Result output unit 201 External measure / Inner measure calculation means 202 Constant density information calculation means 203 Probability distribution calculation means 204 External measure / Inner measure Evaluation value calculation means 205 Time-series data evaluation value calculation means

Claims (14)

Time-series data {ξ ₀ , ξ ₂ , ξ ₃ , ..., ξ _n } with a data length of n + 1 with n as a positive integer is ξ _k = τ (ξ _k-1 ) = τ ^k by the map τ. When generated as (ξ ₀ ), _k = 1, 2, ..., N, the division section X _i (i = 1, 2, ...・ ・ For m), an external measure / inner measure calculation means for obtaining an external measure and a simultaneous external measure as well as an internal measure and a simultaneous internal measure for data having a subdivided section X _j obtained by further dividing each divided section into M equal parts. When,
Based on the external measure and the simultaneous external measure, the constant density simultaneous external measure when the data density is constant and the i-fixed external measure total frequency are obtained, and the data density is calculated based on the internal measure and the simultaneous internal measure. A constant density information calculation means for obtaining a constant density simultaneous internal measure and i-fixed internal measure total frequency when the value is constant.
Based on the constant density simultaneous external measure and the i-fixed external measure total frequency, the external measure probability distribution related to the external measure and the external measure conditional probability distribution when the data density is constant are obtained, and the constant density simultaneous internal measure is obtained. And the probability distribution calculation means for obtaining the internal measure conditional probability distribution when the internal measure probability distribution and the data density are constant for the internal measure based on the i-fixed internal measure total frequency.
The external measure data evaluation value related to the external measure is obtained based on the external measure probability distribution and the external measure conditional probability distribution, and the internal measure data evaluation value related to the internal measure based on the internal measure probability distribution and the internal measure conditional probability distribution. External measure / inner measure evaluation value calculation means to obtain
A time-series data evaluation device comprising: a time-series data evaluation value calculation means for calculating an evaluation value of the entire time-series data based on the outer measure data evaluation value and the inner measure data evaluation value. The outer measure is represented by the value c ₁ [i] of the outer measure counter c ₁ [i], and the simultaneous outer measure is represented by the value c ₂ [i] [j] of the simultaneous outer measure counter c ₂ [i] [j]. When the internal measure is represented by the value c ₃ [i] of the internal measure counter c ₃ [i], and the simultaneous internal measure is represented by the value c ₄ [i] [j] of the simultaneous internal measure counter c ₄ [i] [j]. ,
The time according to claim 1, wherein the constant density information calculation means obtains the outer measure total frequency n by the following formula (01) and the inner measure total frequency n ^* by the following formula (02). Series data evaluation device.

The constant density information calculation means uses the following equation (03) as the constant density simultaneous outer measure d ₂ [i] [j] and the fixed outer measure total measure t ₂ [i] when the data density is constant. In addition to being obtained by equation (05), the constant density simultaneous internal measure d ₄ [i] [j] and the fixed internal measure total measure t ₄ [i] when the data density is constant are expressed by equation (04) and equation (04). The time-series data evaluation device according to claim 1 or 2, wherein the time-series data evaluation device is obtained according to 06).
For i = 1, 2, ..., m, j = 1, 2, ..., m × M

For i = 1, 2, ..., m

The probability distribution calculation means uses the following equation (07) to calculate the external measure probability distribution p _out (i) relating to the external measure and the external measure conditional probability distribution _p'out (j | i) when the data density is constant. In addition to _obtaining by equations (08) and (09), the inner measure probability distribution pinn (i) regarding the inner measure and the inner measure conditional probability distribution _p'inn (j | i) when the data density is constant are as follows. The time-series data evaluation device according to any one of claims 1 to 3, wherein the time-series data evaluation device is obtained by the formula (010), the formula (011), and the formula (012).

When the outer measure / inner measure evaluation value calculation means obtains the outer measure data evaluation value related to the outer measure, the outer measure data evaluation intermediate value h by the following equations (013) and (014) prior to this. When the _out is obtained and the inner measure data evaluation value related to the inner measure is obtained, the inner measure data evaluation intermediate value h _inn is obtained by the following equations (015) and (016) prior to this. The time-series data evaluation device according to any one of claims 1 to 4.

The outer measure / inner measure evaluation value calculation means obtains the outer measure data evaluation value H ^* _out based on the outer measure data evaluation intermediate value h _out by the following formula (017), and is based on the inner measure data evaluation intermediate value h _inn . The time-series data evaluation device according to claim 5, wherein the inner measure data evaluation value H ^* _inn is obtained by the following formula (018).

The time-series data evaluation value calculation means is characterized in that the evaluation value of the entire time-series data is calculated by an operation of obtaining the average of the external measurement data evaluation value and the internal measurement data evaluation value. The time series data evaluation device according to any one of 6. Computer,
Time-series data {ξ ₀ , ξ ₂ , ξ ₃ , ..., ξ _n } with a data length of n + 1 with n as a positive integer is ξ _k = τ (ξ _k-1 ) = τ ^k by the map τ. When generated as (ξ ₀ ), _k = 1, 2, ..., N, the division section X _i (i = 1, 2, ...・ ・ For m), an external measure / inner measure calculation means for obtaining an external measure and a simultaneous external measure as well as an internal measure and a simultaneous internal measure for data having a subdivided section X _j obtained by further dividing each divided section into M equal parts. ,
Based on the external measure and the simultaneous external measure, the constant density simultaneous external measure when the data density is constant and the i-fixed external measure total frequency are obtained, and the data density is calculated based on the internal measure and the simultaneous internal measure. Constant density information calculation means for obtaining constant density simultaneous internal measure and i fixed internal measure total frequency when constant
Based on the constant density simultaneous external measure and the i-fixed external measure total frequency, the external measure probability distribution related to the external measure and the external measure conditional probability distribution when the data density is constant are obtained, and the constant density simultaneous internal measure is obtained. And a probability distribution calculation means for obtaining an internal measure conditional probability distribution when the internal measure probability distribution and the data density are constant for the internal measure based on the i-fixed internal measure total frequency.
The external measure data evaluation value related to the external measure is obtained based on the external measure probability distribution and the external measure conditional probability distribution, and the internal measure data evaluation value related to the internal measure based on the internal measure probability distribution and the internal measure conditional probability distribution. External measure / inner measure evaluation value calculation means,
A time-series data evaluation program characterized by functioning as a time-series data evaluation value calculation means for calculating an evaluation value of the entire time-series data based on the outer measure data evaluation value and the inner measure data evaluation value. The outer measure is represented by the value c ₁ [i] of the outer measure counter c ₁ [i], and the simultaneous outer measure is represented by the value c ₂ [i] [j] of the simultaneous outer measure counter c ₂ [i] [j]. When the internal measure is represented by the value c ₃ [i] of the internal measure counter c ₃ [i], and the simultaneous internal measure is represented by the value c ₄ [i] [j] of the simultaneous internal measure counter c ₄ [i] [j]. ,
The computer is characterized in that, as the constant density information calculation means, the outer measure total frequency n is obtained by the following formula (01), and the inner measure total frequency n ^* is obtained by the following formula (02). The time-series data evaluation program according to claim 8.

Using the computer as the constant density information calculation means, the constant density simultaneous external measure d ₂ [i] [j] and the fixed external measure total measure t ₂ [i] when the data density is constant are expressed by the following equations. In addition to being obtained by equations (03) and equation (05), the constant density simultaneous internal measure d ₄ [i] [j] and the fixed internal measure total measure t ₄ [i] when the data density is constant are expressed in equation (04). ) And the time-series data evaluation program according to claim 8 or 9, wherein the program functions as required by the formula (06).
For i = 1, 2, ..., m, j = 1, 2, ..., m × M

Using the computer as the probability distribution calculation means, the outer measure probability distribution p _out (i) relating to the outer measure and the outer measure conditional probability distribution _p'out (j | i) when the data density is constant are expressed by the following equations. (07), equation (08), equation (09), inner measure probability distribution p _inn (i) for inner measure and inner measure conditional probability distribution _p'inn (j | The time-series data evaluation program according to any one of claims 8 to 10, wherein i) functions as obtained by the following equations (010), (011), and (012).

When the computer is used as the outer measure / inner measure evaluation value calculation means to obtain the outer measure data evaluation value related to the outer measure, prior to this, the outer measure data according to the following equations (013) and (014) are used. When the evaluation intermediate value h _out is obtained and the inner measure data evaluation value related to the inner measure is obtained, the inner measure data evaluation intermediate value h _inn by the following equations (015) and (016) is obtained prior to this. The time-series data evaluation program according to any one of claims 8 to 11, wherein the program is to function as such.

Using the computer as a means for calculating the outer measure / inner measure evaluation value, the outer measure data evaluation value H ^* _out is obtained by the following formula (017) based on the outer measure data evaluation intermediate value h _out , and the inner measure data evaluation intermediate value is obtained. The time-series data evaluation program according to claim 12, wherein the inner measure data evaluation value H ^* _inn is made to function so as to be obtained by the following equation (018) based on h _inn .

The computer is made to function as the time-series data evaluation value calculation means to calculate the evaluation value of the entire time-series data by an operation of obtaining the average of the external measurement data evaluation value and the internal measurement data evaluation value. The time-series data evaluation program according to any one of claims 8 to 13.

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