Data conversion method, data conversion device, data conversion program, and computer readable storage medium storing data conversion program

Abstract

To achieve both of clustering that accompanies dimensional reduction, and restoration of a data space before the dimensional reduction.SOLUTION: A data conversion method includes: a process which classifies each of input data sets 31 into D pieces (D is a natural number of two or more) of clusters by applying soft clustering to the input data sets 31, and outputs gravity center data sets 33 containing a gravity center C of each cluster, and a belonging level data set 32 containing D-dimensional data indicating a belonging probability P to each cluster for each input data set 31a; and a process which outputs a principal component data set 34 which is obtained by dimensional reduction from D-dimensional data to D-1-dimensional data by applying principal component analysis to the belonging level data set 32.SELECTED DRAWING: Figure 4A

Description

[Technical Field]

[0001] The present disclosure relates to a data conversion method, a data conversion device, a data conversion program, and a computer-readable storage medium storing the data conversion program. [Background technology]

[0002] Patent Document 1 discloses a water treatment plant control system as an example of a data conversion method. Specifically, the water treatment plant control system disclosed in Patent Document 1 has a principal component data creation function and an operating state identification function.

[0003] The principal component data creation function performs principal component analysis on plant operation data to create statistical data with a small number of dimensions, and the operational state identification function performs fuzzy c-means clustering on the created statistical data to determine state attribution. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2003-140712 Summary of the Invention [Problem to be solved by the invention]

[0005] When using the method described in Patent Document 1, clustering is performed after principal component analysis is performed on a predetermined data set. Here, when a multivariate data set is used, it is possible to perform dimensionality reduction during principal component analysis, as described in Patent Document 1.

[0006] However, once a dataset has been subjected to dimensionality reduction, it is difficult to restore it. Therefore, even if the clustering results are analyzed and desired principal component scores are found, it is not easy to restore the data structure before dimensionality reduction from the principal component space and arrive at the desired dataset.

[0007] The present disclosure has been made in view of the above points, and its purpose is to achieve both clustering involving dimensionality reduction and restoration of the data structure before dimensionality reduction. [Means for solving the problem]

[0008] A first aspect of the present disclosure relates to a data transformation method for transforming an input data set made up of a plurality of input data each having a plurality of variables by using an arithmetic unit of a computer.

[0009] According to the first aspect, the data conversion method includes the calculation unit performing soft clustering on the input dataset to classify each of the input datasets into D clusters (D is a natural number equal to or greater than 2), and outputting a centroid dataset including the centroids of the D clusters and a membership dataset including D-dimensional data indicating the probability of belonging to each of the D clusters for each of the input data, and the calculation unit performing principal component analysis on the membership dataset to output a principal component dataset in which the D-dimensional data has been reduced to D-1 dimensional data.

[0010] According to the first aspect, the calculation unit generates D-dimensional data by soft clustering, and then reduces the dimension of the D-dimensional data to D-1-dimensional data by principal component analysis. This allows the dimension of each membership probability to be reduced by principal component analysis while maintaining the soft-clustered state.

[0011] Here, the sum of the membership probabilities obtained by soft clustering for each sample (input data) is 1 (=100%). In other words, the membership dataset corresponds to a hyperplane (D-1 dimensional plane) in a D dimensional space. The membership dataset can be essentially regarded as a collection of D-1 dimensional data.

[0012] Therefore, even if the dimension is reduced to D-1 by principal component analysis, the hyperplane is merely rotated so as to align with the D-1 dimensional plane. Therefore, for example, by using the inverse matrix of the rotation matrix, the data structure before the dimension reduction can be restored.

[0013] In this way, according to the first aspect, it is possible to achieve both clustering involving dimensionality reduction and restoration of the data structure before dimensionality reduction.

[0014] Furthermore, according to a second aspect of the present disclosure, the centroids may be provided for each variable constituting the input data, and the calculation unit may calculate, for each variable, differences between centroids belonging to different clusters among the centroids of each of the D clusters, and the calculation unit may output, based on the differences, an index characterizing the differences between the different clusters as a centroid contribution data set for each cluster and for each variable.

[0015] The "difference" here may be the distance between tensors and the numerical data corresponding to that distance.

[0016] According to the second aspect, the calculation unit calculates and outputs the index based on the difference between the centers of gravity obtained as a by-product of the soft clustering process, rather than the difference between the raw data (input data) that was the subject of the soft clustering process.

[0017] This allows for the extraction of features on a cluster-by-cluster and variable-by-variable basis, rather than on the individual features of the input data, enabling more systematic analysis. This more systematic analysis contributes to the exploration of engineering phenomena and intellectual discovery. Furthermore, extraction on a cluster-by-cluster basis provides a more easily recognizable representation when visualizing the extraction results.

[0018] According to a third aspect of the present disclosure, the calculation unit may visualize the index in association with the centroid dataset or the input dataset.

[0019] According to the third aspect, by associating an index with a centroid or an index with input data, it is possible to visualize features and events that appear in centroid units (i.e., cluster units) or to visualize features and events that appear individually in input data units (i.e., sample units), which contributes to realizing visualization with excellent visibility.

[0020] Furthermore, according to a fourth aspect of the present disclosure, the calculation unit may obtain a rotation matrix from a D-dimensional space to which the membership dataset belongs to a principal component space to which the data after principal component analysis belongs, and the calculation unit may convert the index using the rotation matrix, thereby outputting the index as a feature dataset in which the dimension of the D-dimensional data has been reduced to D-1-dimensional data and which includes features for each variable.

[0021] According to the fourth aspect, by acquiring the above-described feature quantities, it becomes possible to directly analyze the contribution of each variable to each principal component score. This enables analysis from various perspectives and also increases the options for visualization in the principal component space. This contributes to the realization of visualization with excellent visibility and, ultimately, to analysis based on the visualization content.

[0022] According to a fifth aspect of the present disclosure, the calculation unit may visualize the feature amounts in association with the input data set for each of the variables.

[0023] According to the fifth aspect, the contribution of each input data before soft clustering to each principal component score can be analyzed. This enables analysis from various perspectives and also increases the options for visualization in the principal component space. This contributes to the realization of visualization with excellent visibility and, ultimately, to analysis based on the visualization content.

[0024] According to a sixth aspect of the present disclosure, the calculation unit may visualize a variable axis corresponding to the feature amount in association with a principal component axis in the principal component dataset.

[0025] According to the sixth aspect, by performing visualization as in this aspect, it is possible to visualize the correlation between a variable corresponding to any feature (or a variable related to the variable) and the principal component score, which contributes to realizing visualization with excellent visibility and, in turn, analysis based on the visualized content.

[0026] Furthermore, according to a seventh aspect of the present disclosure, the calculation unit may acquire a rotation matrix from the D-dimensional space to which the membership dataset belongs to a principal component space to which the data after principal component analysis belongs, the calculation unit may accept a designation of an arbitrary point in the principal component space, the calculation unit may transform the point from the principal component space to a point in the D-dimensional space based on the rotation matrix, and the calculation unit may convert the transformed point into data composed of the plurality of variables based on the probability of belonging to each of the D clusters and the center of gravity of each cluster assigned to each of the variables, and output the converted data.

[0027] According to the seventh aspect, any point specified in the principal component space can be converted into data in the data space to which the input data belongs and output. This allows the user to obtain data in the same format as the input data simply by finding the desired point in the principal component space. This enables analysis based on the principal component space.

[0028] The seventh aspect makes good use of the fact that the data structure can be restored. In addition, by combining it with the sixth aspect, it becomes convenient for searching for the arbitrary point, and enables analysis from a different perspective than conventional ones.

[0029] Also, according to the eighth aspect, the calculation unit may extend the membership probability to a range that allows negative values ​​and values ​​greater than 1, based on the input data set and the centroid data set.

[0030] According to the eighth aspect, by expanding the domain of the membership probability, it becomes possible to perform analysis with a greater degree of freedom, which is advantageous for analysis based on the principal component space and for restoring the data structure from the principal component space.

[0031] Furthermore, according to a ninth aspect of the present disclosure, the variables and the center of gravity may each be time series data in which multiple numerical values ​​are arranged in a time series, and the index may be calculated for each numerical value constituting the time series data.

[0032] According to the ninth aspect, the influence of the passage of time can be taken into account in various analyses, thereby enabling visualization and analysis from various perspectives.

[0033] According to a tenth aspect of the present disclosure, the calculation unit may perform the soft clustering by using a c-means algorithm.

[0034] The "c-means method" referred to here refers to the so-called "Fuzzy c-means method."

[0035] According to the tenth aspect, the belonging probability and the centroid are calculated simply by specifying the number of clusters D. This is advantageous for various processes and analyses based on the belonging probability and the centroid, such as the various visualizations described above.

[0036] An eleventh aspect of the present disclosure relates to a data conversion device that converts an input data set made up of a plurality of input data each having a plurality of variables by using a calculation unit of a computer.

[0037] According to the eleventh aspect, the data conversion device comprises: means for performing soft clustering on the input datasets to classify each of the input datasets into D clusters (D is a natural number equal to or greater than 2), and outputting a centroid dataset including the centroids of the D clusters and a membership dataset including D-dimensional data indicating the probability of each of the input data belonging to each of the D clusters; and means for performing principal component analysis on the membership datasets to output a principal component dataset in which the D-dimensional data has been reduced to D-1 dimensional data.

[0038] According to the eleventh aspect, it is possible to achieve both clustering involving dimensionality reduction and restoration of the data structure before dimensionality reduction.

[0039] A twelfth aspect of the present disclosure relates to a data conversion program that, when executed by a calculation unit of a computer, converts an input data set made up of a plurality of input data each having a plurality of variables.

[0040] According to the twelfth aspect, the data conversion program causes the computer to execute the following processes: the calculation unit performs soft clustering on the input datasets to classify each of the input datasets into D clusters (D is a natural number equal to or greater than 2), and outputs a centroid dataset including the centroids of each of the D clusters, and a membership dataset including D-dimensional data indicating the probability of each of the input data belonging to each of the D clusters; and the calculation unit performs principal component analysis on the membership datasets to output a principal component dataset in which the D-dimensional data has been reduced to D-1 dimensional data.

[0041] According to the twelfth aspect, it is possible to achieve both clustering involving dimensionality reduction and restoration of the data structure before dimensionality reduction.

[0042] A thirteenth aspect of the present disclosure relates to a computer-readable storage medium that stores the data conversion program.

[0043] According to the thirteenth aspect, it is possible to achieve both clustering involving dimensionality reduction and restoration of the data structure before dimensionality reduction. [Effects of the Invention]

[0044] As described above, according to the present disclosure, it is possible to achieve both clustering involving dimensionality reduction and restoration of the data structure before dimensionality reduction. [Brief explanation of the drawings]

[0045] [Figure 1] FIG. 1 is a diagram illustrating an example of a hardware configuration of a data conversion device. [Figure 2] FIG. 2 is a diagram illustrating an example of the software configuration of the data conversion device. [Figure 3] FIG. 3 is a flowchart illustrating the procedure of the data conversion method. [Figure 4A] FIG. 4A is a block diagram illustrating inputs and outputs in a data transformation method. [Figure 4B] FIG. 4B is a block diagram illustrating inputs and outputs in a data transformation method. [Figure 4C] FIG. 4C is a block diagram illustrating inputs and outputs in a data transformation method. [Figure 5] FIG. 5 is a diagram conceptually illustrating an input data set. [Figure 6] FIG. 6 is a flowchart illustrating the steps of the clustering process. [Figure 7] FIG. 7 is a diagram showing a specific example of the attribution degree dataset. [Figure 8] FIG. 8 is a flowchart illustrating the steps of the PCA process. [Figure 9] FIG. 9 is a diagram showing a specific example of a principal component data set. [Figure 10] FIG. 10 is a diagram illustrating the steps of the feature extraction process. [Figure 11] FIG. 11 is a diagram illustrating the first and fourth visualization processes. [Figure 12] FIG. 12 is a diagram illustrating the second visualization process. [Figure 13] FIG. 13 is a diagram illustrating the second visualization process. [Figure 14] FIG. 14 is a diagram illustrating the third visualization process. [Figure 15] FIG. 15 is a flowchart illustrating the steps of the data generation process. [Figure 16] FIG. 16 is a diagram for explaining the extended belonging probability. DETAILED DESCRIPTION OF THE INVENTION

[0046] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. Note that the following description is for illustrative purposes only.

[0047] <1.Device configuration> FIG. 1 is a diagram illustrating an example of the hardware configuration of a data conversion device according to the present disclosure (specifically, a computer 1 constituting the data conversion device), and FIG. 2 is a diagram illustrating an example of the software configuration thereof.

[0048] 1, the computer 1 includes a central processing unit (CPU) 3 that controls the entire computer 1, a read only memory (ROM) 5 that stores a boot program and the like, a random access memory (RAM) 7 that functions as a main memory, and a solid state drive (SSD) 9 that serves as a secondary storage device. Note that a hard disk drive (HDD) or the like can also be used as the secondary storage device instead of the SSD 9.

[0049] Of these elements, the CPU 3 executes various programs. The CPU 3 functions as a calculation unit in this embodiment. The RAM 7 and SSD 9 temporarily or continuously store the programs executed by the CPU 3. The RAM 7 and SSD 9 each function as a storage unit in this embodiment.

[0050] The computer 1 also includes a display 11, a graphics memory (Video RAM: VRAM) 13 that stores image data to be displayed on the display 11, and a keyboard 15 and a mouse 17 as man-machine interfaces. The keyboard 15 and the mouse 17 function as a reception unit that receives input from an operator. The display 11 can display a screen based on the results of calculations by the CPU 3, and functions as a display unit in this embodiment. The computer 1 according to this embodiment can also send and receive data to and from external devices via a communication interface 19.

[0051] As illustrated in FIG. 2, the program memory of SSD 9 stores an operating system (OS) 21, a clustering program 231, a PCA program 232, a centroid analysis program 233, a visualization program 234, a data generation program 235, an application program 25, etc.

[0052] Of these programs, the clustering program 231, the PCA program 232, the centroid analysis program 233, the visualization program 234, and the data generation program 235 constitute the data conversion program 23 in this embodiment.

[0053] Here, the data conversion program 23 is a program for executing a data conversion method described below, and is configured to cause the computer 1 to execute each step constituting the method. The data conversion program 23 is pre-stored in a computer-readable storage medium 18. This storage medium 18 is a tangible storage medium constituted by a disk medium or the like.

[0054] In the program memory of the SSD 9, each program constituting the data conversion program 23 is started in response to a command input from the keyboard 15, the mouse 17, etc. At that time, each program is loaded from the SSD 9 into the RAM 7 and executed by the CPU 3.

[0055] Meanwhile, the data memory of the SSD 9 stores an input dataset 31, a membership dataset 32, a centroid dataset 33, a principal component dataset 34, rotation matrix data 35, a centroid contribution dataset 36, and a feature dataset 37, all of which will be described later. These will be described in detail later.

[0056] In addition, various data generated by executing the clustering program 231, PCA program 232, center of gravity analysis program 233, visualization program 234, and data generation program 235, as well as the execution results of the application program 25, are stored in the data memory of the SSD 9 or in the RAM 7 as the main memory, as necessary.

[0057] The specific methodology of the data conversion method will be described in detail below.

[0058] <2. Overview of data conversion method> Fig. 3 is a flowchart illustrating the steps of the data conversion method. Fig. 4A, Fig. 4B, and Fig. 4C are block diagrams illustrating inputs and outputs in the data conversion method. Fig. 5 is a diagram for conceptually explaining the input data set 31.

[0059] This data conversion method uses the CPU 3 of the computer 1 to convert an input data set 31 and output the conversion results.

[0060] Here, the input dataset 31 is a dataset made up of a plurality of input data 31a (see FIG. 5). Hereinafter, the number of pieces of input data 31a is assumed to be N (N is a natural number equal to or greater than the total number D of clusters, which will be described later). In this case, the input dataset 31 can be regarded as a dataset with N samples (N samples).

[0061] 5, each of the plurality of input data 31a has a plurality of variables 31b. Hereinafter, the number of variables 31b is assumed to be M (M is a natural number equal to or greater than 1). In this case, each of the input data 31a can be regarded as data of M variables.

[0062] 5, each of the multiple variables 31b is a data series in which multiple numerical values ​​are arranged. Specifically, each of the multiple variables 31b according to this embodiment is time-series data in which multiple numerical values ​​are arranged in a time series. Hereinafter, the number of data points (number of periods) in the series direction (time direction) is set to L (L is a natural number equal to or greater than 1). In this case, each variable 31b can be considered as time-series data with the number of series L (L series).

[0063] Note that the number of sequences L is not necessarily the same for each sample. The number of sequences L may be different for each sample. Furthermore, the time intervals in each time series data may also be different for each sample. For example, when each variable 31b indicates measurement data, the measurement period of the measurement data may be different for each sample, and the measurement interval of the measurement data may be different for each sample.

[0064] Hereinafter, n is a natural number between 3 and N, m is a natural number between 2 and M, and l is a natural number between 1 and L. In this case, the input data set 31 is a third-order tensor "x" representing the l-th data in the m-th variable 31b in the n-th input data 31a. nml (∈R)".

[0065] In the following, for the sake of brevity, some indices may be omitted. For example, if there is no need to mention the sequence direction, the above tensor is written as "x nm Even in this case, the meanings of "l", "m" and "n" are the same.

[0066] Furthermore, in this embodiment, time-series data of M variables that characterize vehicle behavior is used as a specific example of each input data 31a. Each of the M variables 31b indicates time-series data measured at M locations. Each time-series data (variable 31b) indicates the amount of vertical displacement of the vehicle at each measurement location. In particular, in this embodiment, when the vehicle runs over a specific structure (for example, a protrusion or a slope), the amount of vertical displacement before and after the vehicle runs over the structure is used as the amount of vertical displacement. In other words, "data value x = displacement amount".

[0067] In this embodiment, the input data 31a is measured a total of 16 times for three vehicle types. That is, in this specific example, the "number of samples N=16." The first vehicle type is measured five times, the second vehicle type is measured five times, and the other vehicle type (hereinafter collectively referred to as the "third vehicle type") is measured six times.

[0068] Returning to Figure 3, as shown in the figure, the data conversion method is implemented by sequentially executing a clustering process (step S1), a PCA process (step S2), a centroid analysis process (step S3), a visualization process (step S4), and a data generation process (step S5).

[0069] Of these processes, the centroid analysis process (step S3), the visualization process (step S4), and the data generation process (step S5) are not essential. The order of execution of these processes may be changed as appropriate, and one or more of these processes may be executed simultaneously.

[0070] The data conversion program 23 is configured to cause the computer 1 to execute these processes. That is, of the processes described above, the clustering process is performed by the CPU 3 executing the clustering program 231. Similarly, the PCA process is performed by the CPU 3 executing the PCA program 232. The feature extraction process is performed by the CPU 3 executing the feature extraction program 233. The visualization process is performed by the CPU 3 executing the visualization program 234. The data generation process is performed by the CPU 3 executing the data generation program 235.

[0071] When the CPU 3 executes the clustering program 231 etc., the computer 1 constitutes a data conversion device. That is, the computer 1 functions as a data conversion device including a clustering means for executing a clustering process and a PCA means for executing a PCA process. The computer 1 as a data conversion device further includes, as necessary, a feature extraction means for executing a feature extraction process, a visualization means for executing a visualization process, and a data generation means for executing a data generation process.

[0072] Each process constituting the data conversion method will be explained in order below. Please refer to Figures 4A to 4C as appropriate for the input and output of data sets in each process, the meaning of the rank and each component when each data set is considered as a tensor, and the relationship between each data set and each program.

[0073] (2-1. Clustering process) Fig. 6 is a flowchart illustrating the procedure of the clustering process. Fig. 7 is a table showing a specific example of the membership dataset 32. Fig. 7 is a table showing a specific example of soft clustering. When the control process proceeds to step S1 in Fig. 3, the CPU 3 executes each step in order from step S11 in Fig. 6.

[0074] The clustering step according to this embodiment is configured so that the CPU 3 performs soft clustering on the input dataset 31. In this clustering step, the CPU 3 classifies each of the input datasets 31 into D clusters (D is a natural number of 2 or more), and outputs a membership dataset 32 ​​and a centroid dataset 33.

[0075] The total number D of clusters is set in advance. The CPU 3 sets the value of the total number D based on the contents stored in advance in a storage unit such as the SSD 9, or on operational input via the keyboard 15 or the mouse 17 as an operation unit. In the specific example described above, the total number D is set to "D=3."

[0076] Here, the membership data set 32 ​​includes D-dimensional data for each input data 31a or sample that constitutes the input data set 31. This D-dimensional data represents the probability of belonging to each of the D clusters P(∈R N×D ) and the centroid data set 33 shows the centroid C(∈R D×M×L )

[0077] Hereinafter, d is a natural number that is equal to or greater than 1 and equal to or less than D. In this case, the probability that the n-th input data 31a belongs to the d-th cluster is expressed as a second-order tensor "P nd Each probability P nd is a real number, and the sum of the probabilities of belonging to each cluster given to the nth input data is 1.

[0078] The center of gravity C is given as a multivariate data series, similar to each input data 31a constituting the input data set 31. Specifically, the center of gravity C is given for each variable 31b constituting the input data 31a. More specifically, the center of gravity C corresponding to each variable 31b is time-series data in which multiple data are arranged in a time series. Furthermore, the center of gravity C is given for each cluster.

[0079] Therefore, the centroid C for the d-th cluster is expressed as "C dml ". In addition, when expressing the center of gravity C, in order to omit the type of variables and / or the order of the time series direction, "C dm " or "C d " It can also be expressed as ".

[0080] Hereinafter, to clarify the meaning of the subscripts of each tensor, the input data 31a corresponding to each subscript n may be referred to as "each sample n," the variable 31b corresponding to each subscript m may be referred to as "each variable m," the time corresponding to each subscript l may be referred to as "each time l," and the cluster corresponding to each subscript d may be referred to as "each cluster d." These names are merely provisional names for the convenience of explanation, and do not limit the meaning of each subscript n, m, l, d, such as limiting the subscript l to time, or the meaning of the input data set 31 and the input data 31a.

[0081] Returning to Figure 6, in step S11, the CPU 3 reads the input data set 31. Once this reading is complete, the CPU 3 advances the control process to step S12.

[0082] In the following steps S12 to S15, the CPU 3 performs soft clustering on the input data set 31 read in step S11. Soft clustering is a method that allows each piece of input data 31a to belong to one or more clusters.

[0083] The CPU 3 performs soft clustering to calculate the degree of belonging to each cluster for each of the plurality of input data 31a as the belonging probability P. Here, each input data 31a is classified so as to belong to one or more clusters. This means that for each input data 31a, each component P constituting the belonging probability P is calculated. nd This means that the sum of d is 1 (=100%) for each cluster (see the formula below). In other words, the degrees of freedom for each cluster are effectively "D-1" rather than "D".

[0084]

number

[0085] In this embodiment, the CPU 3 performs soft clustering using the c-means method (also called the Fuzzy C-Means method). Any other method may be used as long as it is capable of outputting the degree of belonging to each cluster and the center of gravity (also called the center or centroid) from the degree of belonging. Hereinafter, the "c-means method" will also be referred to as the "FCM method."

[0086] When executing the FCM method, the CPU 3 randomly initializes each component of the belonging probability P in step S12. This differs from the k-means method in that the belonging probability P is initialized instead of the center of gravity C.

[0087] In the following step S13, the CPU 3 calculates the center of gravity C of each cluster based on the current belonging probability P (see the following formula): In the following formula, f is a parameter (fuzzy parameter) that satisfies f>1.

[0088]

number

[0089] As shown in the above formula, the calculation of the center of gravity C is performed not only for each cluster distinguished by d=1, . . . , D, but also for each variable m and each time 1.

[0090] In the next step S14, the CPU 3 calculates the center of gravity C dml The belonging probability P is updated based on the value of the center of gravity C calculated in step S13 and each x lmn This calculation is performed for each different cluster.

[0091] Here, the subscript m for distinguishing the type of each variable 31b may be added up from m=1 to m=M, as in the general Frobenius norm.

[0092] However, with regard to the subscripts l used to distinguish the time series of each variable 31b, the total number L of subscripts l and the time intervals between each subscript l may differ for each sample n. If the total number L or the like differs for each sample n, the difference between different times must be used when calculating the distance as described above.

[0093] Therefore, the CPU 3 according to this embodiment calculates the difference between the variables 31b or the difference between the variable 31b and the center of gravity C dml When calculating the difference between the two, the data is linked using alignment matrix A.

[0094] For example, CPU3 has two variables x i and y j’ When calculating the distance Di between

[0095]

number

[0096] In the above equation, Δ(x, y) represents the cost matrix. The ij component of the cost matrix is ​​x i and y j The distance function δ(x i ,y j), and A is the alignment matrix. Each component of A is either 0 or 1. If i = 1, ..., I and j = 1, ..., J, then both the cost matrix and the alignment matrix can be expressed as a matrix with I rows and J columns. < > is the inner product of the matrices (the sum of the products of each component). The above formula means that the alignment matrix with the smallest inner product is searched for from a set of candidate alignment matrices, and the smallest value is taken as the distance.

[0097] If the off-diagonal elements of the alignment matrix are non-zero, then x for i ≠ j i and y j The distance between the two tensors is given. This allows us to associate the index i (e.g., the i-th time) of one tensor with the index j (e.g., the j-th time) of the other tensor when calculating the distance between two tensors. If there are multiple non-zero column components in the i-th row of the alignment matrix A, multiple j-th times will be associated with the i-th time.

[0098] For example, as in the specific example described above, when different vehicle models are the measurement targets, it is conceivable that the sensors on each vehicle body will perform measurements at different times and that the measurement periods will also differ.

[0099] In contrast, by using the alignment matrix, it is possible to provide a more flexible expression. More specifically, in this embodiment, the above-mentioned DTW (Dynamic Time Warping) method is used as the method using the inner product. Instead of this DTW method, the GAK method, soft-DTW method, modified soft-DTW method, etc. can be used.

[0100] The alignment matrix can also be used to calculate the center of gravity C. As an example, consider a case where the number L of time points l differs for each sample n. In that case, the above-described definition of the center of gravity C can no longer be used.

[0101] Therefore, when the number of Ls differs for each sample n, the CPU 3 according to this embodiment matches the number of Ls at the center of gravity C of each cluster d with the minimum value of Ls in that cluster. lmn For x at multiple times l, lmn The values ​​of l are combined (for example, averaged) to reduce the number of L's at that sample n. When selecting multiple times l, non-zero elements in the alignment matrix can be used.

[0102] Then, in the following step S15, the CPU 3 calculates the difference between the membership probability P before and after the update (for example, the norm between tensors) and determines whether or not the difference is equal to or less than a predetermined variable ε. This difference may be calculated using an alignment matrix, similar to the membership probability P.

[0103] If the determination in step S15 is YES, the CPU 3 advances the control process to step S16, whereas if the determination is NO, the CPU 3 returns the control process to step S13. When returning to step S13, the CPU 3 recalculates the center of gravity C based on the belonging probability P updated in step S14.

[0104] In step S16, the CPU 3 outputs the membership dataset 32 ​​and the centroid dataset 33. The membership dataset 32 ​​is the latest belonging probability P at the time when the determination in step S15 is YES. On the other hand, the centroid dataset 33 is the latest centroid C at the time when the determination in step S15 is YES.

[0105] In the above-mentioned specific example, the belonging degree data set 32 ​​as shown in FIG. 7 is output. 16 samples are classified into three different clusters. Three-dimensional data (belonging probability P) is given for each sample n. The belonging probability P for each sample n is a non-zero value for each of the three clusters. Also, as shown in the figure, the sum of the belonging probabilities P for each sample n is 1.

[0106] For example, the first sample (n=1) can be classified into the first cluster because the probability P of belonging to the first cluster (d=1) is greater than the probability P of belonging to the second cluster (d=2) and the third cluster (d=3).

[0107] Furthermore, the belonging probability P in the first sample is "0.932+0.046+0.022=1", and the sum is 1 (100%).

[0108] Thereafter, the CPU 3 stores the membership data set 32 ​​and the centroid data set 33 output as described above in the RAM 7 or the SSD 9. The stored data sets 32 and 33 are read as needed in subsequent processing such as the PCA process. Once the storage of the data sets 32 and 33 is complete, the CPU 3 advances the control process to step S2 in FIG. 3.

[0109] (2-2. PCA process) Fig. 8 is a flowchart illustrating the procedure of the PCA process. When the control process proceeds to step S2 in Fig. 3, the CPU 3 executes each step in order from step S21 in Fig. 8.

[0110] The PCA step according to this embodiment is configured so that the CPU 3 executes a principal component analysis (PCA) on the membership data set 32. By executing the principal component analysis, the CPU 3 outputs a principal component data set 34 in which the dimensions of each D-dimensional data (membership probability P) are reduced to D-1-dimensional data.

[0111] Here, the principal component data set 34 includes D-1-dimensional data for each input data 31a or sample constituting the input data set 31. This D-1-dimensional data indicates the first principal component to the D-1-th principal component, which correspond to the probability P of belonging to each of the D clusters.

[0112] 8, in step S21, the CPU 3 reads the membership data set 32. When this reading is complete, the CPU 3 advances the control process to step S22.

[0113] In the next step S22, the CPU 3 performs PCA on the membership dataset 32 ​​read in step S21. There are various PCA methods, but the method is not particularly limited. For example, although the following explanation illustrates an eigenvalue problem of a variance-covariance matrix, a method based on singular value decomposition may also be used.

[0114] Specifically, in step S22, the CPU 3 generates a variance-covariance matrix Σ with D rows and D columns based on the membership data set 32. The CPU 3 further diagonalizes the variance-covariance matrix Σ to obtain a total of D eigenvalues ​​(λ1, ..., λ D ) and eigenvectors (ω1,…,ω D )

[0115] In the next step S23, the CPU 3 generates a rotation matrix R with D rows and D columns based on the eigenvectors generated in step S23. In the next step S24, the CPU 3 converts the membership probability P using the rotation matrix R to obtain a principal component score Q for each sample n. nd Calculate.

[0116]

number

[0117] In the above equation, the component R of the rotation matrix R dt is the eigenvector ω d This rotation matrix R corresponds to a rotation matrix from the D-dimensional space to which the belonging probability P belongs to, to the principal component space Sp1 to which each principal component belongs. For details of the principal component space Sp1, see, for example, FIG. 11.

[0118] Principal component score Q nd is D-dimensional data corresponding to D kinds of clusters d. On the other hand, the component P of the belonging probability Pnt With respect to the degree of freedom for cluster d, it can be regarded as a hyperplane (a D-1 dimensional plane) in D-dimensional space. Therefore, the membership probability P nt Principal component score Q calculated from nd The Dth component Q nD The principal component score Q is the same for different samples n. nd can be considered as D-1 dimensional data.

[0119] In the next step S25, the CPU 3 outputs the principal component data set 34 and the rotation matrix data 35. The principal component data set 34 is a set of the principal component scores Q calculated for each sample n and for each cluster d. nd The rotation matrix data 35 is a set of the rotation matrix R described above converted into numerical data.

[0120] In the case of the specific example described above, a principal component data set 34 as shown in Figure 9 is output. For each of the 16 samples n, the principal component score Q corresponding to the first principal component is n1 and the principal component score Q corresponding to the second principal component n2 As mentioned above, the third principal component is meaningless, so it may be set to 0 for all samples or may be excluded from being stored as numerical data.

[0121] Thereafter, the CPU 3 stores the principal component data set 34 and rotation matrix data 35 output as described above in the RAM 7 or the SSD 9. The stored data 34, 35 are read as needed in subsequent processes such as the feature extraction process. Once the storage of the data 34, 35 is complete, the CPU 3 advances the control process to step S3 in FIG. 3.

[0122] (2-3. Feature extraction process) 10 is a flowchart illustrating the procedure of the feature extraction process. When the control process proceeds to step S3 in FIG. 3, the CPU 3 executes each step in order from step S31 in FIG.

[0123] In the feature extraction process according to this embodiment, the CPU 3 calculates the difference σ(∈R D×D×M×L ) for each variable m. The CPU 3 also calculates an index B(∈R D×M×L ) is output as a centroid contribution data set 36 containing the data for each cluster d and each variable m.

[0124] Furthermore, in the feature extraction process, the CPU 3 converts the index B by the rotation matrix R, and converts the index B into a feature S(∈R D-1×M×L ) is output as a feature dataset 37 containing the

[0125] Specifically, in step S31, the CPU 3 reads the center of gravity data set 33 and the rotation matrix data 35. When this reading is completed, the CPU 3 advances the control process to step S32.

[0126] In the next step S32, the CPU 3 calculates the difference σ between the centers of gravity belonging to different clusters d and d′. Here, as described above, if the size L of the time l differs for each sample n and therefore for each center of gravity C, the following formula can be used.

[0127]

number

[0128] In the above formula, "mean(X) y " means the average value of X for each y. Also, "l' = arg(A ll’ ≠0) means that among various l' (l' is a natural number less than or equal to L), "alignment matrix A ll’ means the set of l' that satisfies "≠0".

[0129] The difference is calculated using the alignment matrix for the time series direction (time l direction) of each center of gravity C. This calculation is performed for each different variable m.

[0130] On the other hand, if the subscript l has the same meaning for each center of gravity C, such as the size L (when an alignment matrix is ​​not required), the alignment matrix will be an L-row, L-column identity matrix. In this case, the above formula reduces to a simple difference between centers of gravity, as shown below.

[0131]

number

[0132] Next, in step S33, the CPU 3 calculates an index B for each cluster d and for each variable m based on the difference σ.

[0133]

number

[0134] For example, if D=3 and no alignment matrix is ​​required, the index B1 is C 1ml -C 2ml And, C 1ml -C 3ml As is clear from the fact that index B1 + index B2 + index B3 = 0, the sum of the indices characterizing the differences between different clusters is 0. In other words, although index B is a D-dimensional variable in terms of the cluster degrees of freedom, it can be regarded as a hyperplane in D-dimensional space, just like the membership probability P.

[0135] Next, in step S34, the CPU 3 calculates the index B dml is multiplied by the rotation matrix R to reduce the dimension from the D-dimensional data space to the D-1-dimensional principal component space. dml is the feature S dml Then, it can be expressed as the following equation.

[0136]

number

[0137] The above feature S dml is the principal component score Q nd Similarly, it can be considered as D-1 dimensional data in terms of cluster degrees of freedom. In the case of "D=3" as in the specific example, the feature S corresponding to the first principal component is 1mn and the feature S corresponding to the second principal component 2mn are calculated for each variable m and for each time l.

[0138] In the next step S35, the CPU 3 outputs a centroid contribution data set 36 and a feature data set 37. The centroid contribution data set 36 includes each index B dml The feature dataset 37 is a set of each feature S dml is a set of.

[0139] Thereafter, the CPU 3 stores the centroid contribution data set 36 and the feature data set 37 output as described above in the RAM 7 or the SSD 9. The stored data sets 36 and 37 are read as needed in subsequent processing such as the visualization process. Once the storage of the data sets 36 and 37 is complete, the CPU 3 advances the control process to step S4 in FIG. 3.

[0140] (2-4. Visualization process) Fig. 11 is a diagram illustrating the first and fourth visualization processes. Fig. 12 is a diagram for explaining the second visualization process. Fig. 13 is a diagram illustrating the second visualization process. Fig. 14 is a diagram illustrating the third visualization process.

[0141] 11 to 14 each show an example of a display screen of the display 11 serving as a display unit. These displays are performed by the CPU 3 in the visualization process shown in step S4 of FIG.

[0142] In the visualization process, the CPU 3 performs one or more of the following operations:

[0143] First visualization process: Visualization of principal component dataset 34 Second visualization process: visualization of the centroid data set 33 or the input data set 31 and the centroid contribution data set 36 Third visualization process: Visualization of input dataset 31 and feature dataset 37 Fourth visualization process: Visualization of the principal component dataset 34 and feature dataset 37 The four visualization processes described above will be explained below. The following explanation is based on the specific examples shown in Figures 7 and 9, but as mentioned above, the present disclosure is not limited to application to specific specific examples.

[0144] (2-4-1. First visualization process) 11 shows a specific example of the first visualization process. In this first visualization process, the CPU 3 calculates the principal component scores Q nd are displayed as a scatter plot in the principal component space (a two-dimensional plane in the example). The horizontal axis of Figure 11 is the first principal component axis, and the vertical axis of the same figure is the second principal component axis.

[0145] In Figure 11, each principal component score Q nd are visualized as circular plots. The boxed areas Ci1, Ci2, and Ci3 indicate that the plots belong to the first cluster, the second cluster, and the third cluster, respectively, mentioned in the description of FIG. 7 and other figures.

[0146] (2-4-2. Second visualization process) Subsequently, in the second visualization process, the CPU 3 visualizes the indicator B in association with the centroid data set 36 or the input data set 31. This visualization can be performed for each variable m.

[0147] For example, the upper part of FIG. 12 shows the centroids C that make up the centroid data set 36. dml1 is a graph showing the values ​​of the center of gravity C1 of the first cluster, the center of gravity C2 of the first cluster, and the center of gravity C3 of the third cluster along the time series direction (direction l) for a specific variable m. In the figure, the solid line represents the center of gravity C1 of the first cluster, the dashed-dotted line represents the center of gravity C2 of the second cluster, and the dashed-two-dotted line represents the center of gravity C3 of the third cluster.

[0148] The middle part of Figure 12 shows the indexes B that make up the centroid contribution dataset 36. dml This is a graph showing the index B1 of the first cluster in the same variable m as in the figure, along the time series direction. For simplicity, if we do not consider the alignment matrix, the value of index B1 in this case is C 1ml -C 2ml And, C 1ml -C 3ml The "+" in the figure indicates that the average value is positive. The "-" in the figure indicates that the average value is negative.

[0149] Here, the CPU 3 may display the contents corresponding to the upper and middle rows of FIG. 12 side by side on the screen, or may display the contents corresponding to the respective centers of gravity C dml and the corresponding index B dml The values ​​of m may be displayed overlapping each other. Both cases are included in the "associated visualization" in this application. Both types of association can be performed for each variable m.

[0150] Also, in the lower part of Figure 13, the corresponding index B dml The value of is visualized as a semi-transparent gradient, with different display modes such as color tone and hatching for the "+" and "-" cases. dml The shading of each gradation may be varied depending on the size of the gradation.

[0151] Also, as shown in Figure 13, each center of gravity C dml Value and corresponding indicator B dml Instead of associating values ​​of nml)31a value and index B dml The values ​​of may be associated and visualized.

[0152] For example, FIG. 13 shows the input data set 31. nml The value of and the corresponding index B dml This is a graph showing the values ​​of for a specific variable m, by cluster d, along the time series direction (l direction).

[0153] Here, a positive index B1 suggests that the value of the center of gravity C1 in the first cluster is significantly larger than in the other clusters. A negative index B1 suggests that the value of the center of gravity C1 in the first cluster is significantly smaller than in the other clusters. This suggests that the first cluster has characteristics that are different from the other clusters.

[0154] (2-4-3. Third visualization process) Next, in the third visualization process, the CPU 3 calculates the feature quantity S dml is visualized in association with the input data set 31. This visualization can be performed for each variable m.

[0155] For example, FIG. 14 shows the input data set 31. nml The value (displacement) and the corresponding feature S dml This graph shows the values ​​of each variable m for each principal component along the time series direction (l direction). Each square displays the data values ​​of all samples n (=16).

[0156] The left column of Figure 14 shows the feature S corresponding to the first principal component (d=1). 1ml The right side of Fig. 14 shows the feature S corresponding to the second principal component (d=2). 2ml is the value.

[0157] As in the second visualization process (particularly the lower part of FIG. 12), the CPU 3 nml and the corresponding feature S dmlThe values ​​of m are visualized by overlapping them for each variable m. dml The value of is visualized as a semi-transparent gradient, with different display modes such as color tone and hatching for the "positive" case and the "negative" case. dml The shading of each gradation can be varied depending on the magnitude of the "+" sign. The "-" sign in FIG. 14 corresponds to the "positive" case.

[0158] Although a detailed layout is omitted, the third, fourth, and fifth variables indicate the output values ​​of sensors installed at the front of the vehicle. These variables peak at the beginning of the measurement. This suggests that the vehicle ran over a specific structure, causing an upward displacement at the front of the vehicle, which was detected by each sensor.

[0159] Focusing on the first principal component, the third, fourth, and fifth variables each reach their peaks, and then when the vertical displacement decreases and reaches a minimum value, the value of the feature quantity S shifts significantly to the positive side. This suggests that when the vehicle runs over a structure and is then pulled down and sinks, the third to fifth variables are significantly involved in the magnitude of the first principal component.

[0160] Furthermore, by associating the magnitude of the sinking amount after the peak with the direction of increase or decrease of the feature value S and therefore the first principal component, it is possible to determine the correlation (in particular, whether the correlation is positive or negative) between the first principal component and the physical quantities (sinking amounts) associated with the third to fifth variables.

[0161] Focusing on the second principal component, the third, fourth, and fifth variables each show a large positive shift in the value of the feature quantity S while the vertical displacement is decreasing after reaching the peak. This suggests that the third to fifth variables are significantly involved in the magnitude of the second principal component while the vehicle is being pulled down and sinking after climbing over a structure.

[0162] Furthermore, by relating the slope of the sinking amount after the peak to the direction of increase or decrease of the feature S and therefore the second principal component, it is possible to determine the correlation (in particular, whether the correlation is positive or negative) between the second principal component and the physical quantities (pull-down strength) associated with the third to fifth variables.

[0163] Focusing further on the third, fourth, and fifth variables of the second principal component, the values ​​of the feature quantity S of these variables are significantly shifted to the positive side even at the peak. This suggests that the third to fifth variables are also significantly involved in the magnitude of the second principal component when the vehicle runs over the structure.

[0164] Furthermore, by associating the peak height with the direction of increase or decrease of the feature value S and therefore the second principal component, it is possible to determine the correlation (in particular, whether the correlation is positive or negative) between the second principal component and the physical quantities (peak heights) associated with the third to fifth variables.

[0165] (2-4-4. Fourth visualization process) In the fourth visualization process, the CPU 3 calculates the feature quantity S dml The variable axis Ax corresponding to the input data 31a is visualized in association with the principal component axes in the principal component data set 34. This variable axis Ax may be the value of one or more variables constituting the input data 31a, etc. (for example, the amount of vertical displacement), such as the third to fifth variables, or may be a physical quantity corresponding to one or more variables, as described with reference to FIG.

[0166] As in the example in the lower part of FIG. 12, the level of the corresponding variable or physical quantity of each variable axis Ax may be visualized by varying the shade of color.

[0167] In the example shown, the first principal component axis is the feature S 13l , feature S 14l , feature S 15l The graph is visualized in relation to the variable axis Ax, which indicates the physical quantity A (amount of subsidence) corresponding to the above.

[0168] Similarly, the second principal component axis represents the feature S 23l , feature S 24l , feature S 25l The variable axis Ax indicating the physical quantity B (pulling strength) corresponding to the peak height is visualized in association with the variable axis Ax indicating the physical quantity C (peak height).

[0169] For example, in the case of a vehicle, considering vibrations that occur when the vehicle runs uphill, desired target values ​​(see target point 41 in FIG. 11) may exist for physical quantities A to C. By performing the fourth visualization process, it becomes possible to find the values ​​of each principal component that correspond to such target values.

[0170] However, simply finding the values ​​of each principal component does not necessarily improve usability. To improve usability, it is convenient to restore the data to the same data format as the input data 31a, for example, to values ​​of vertical displacements arranged in a time series direction, as shown in the example of each variable 31b in Figure 14.

[0171] By using the data generation process (step S5) shown in FIG. 3, such needs can be met.

[0172] (2-5. Data generation process) Fig. 15 is a flowchart illustrating the procedure of the data generation process. When the control process proceeds to step S5 in Fig. 3, the CPU 3 executes each step in order from step S51 in Fig. 15.

[0173] First, in step S51, the CPU 3 accepts the designation of a target point 41. As illustrated in FIG. 11, the target point 41 is an arbitrary point in the principal component space Sp1. As illustrated in FIG. 4C, the target point 41 is D-1 dimensional data. This acceptance is performed by accepting an operation input via the mouse 17, the keyboard 15, etc., or by reading a data file generated outside the computer 1.

[0174] In the following step S52, the CPU 3 reads the center of gravity data set 33 and the rotation matrix data 35 from the SSD 9 etc. When this reading is completed, the CPU 3 advances the control process to step S52.

[0175] In the next step S52, the CPU 3 transforms the target point 41 from the principal component space Sp1 into a target belonging degree 42 defined in the same D-dimensional space as the belonging probability P, based on the rotation matrix R.

[0176] As shown in FIG. 4C , the target belonging degree 42 is a point corresponding to the target point 41. The target belonging degree 42 is a D-dimensional vector. Each component of the target belonging degree 42 indicates the probability of belonging to each of the D clusters, similar to the belonging probability P.

[0177] Specifically, in step S53, the CPU 3 multiplies the D-1-dimensional vector corresponding to the target point 41 by the rotation matrix R, and outputs the multiplication result as the target belonging degree .

[0178] In the next step S54, the CPU 3 converts the target points 41 after conversion, that is, the target degrees of belonging 42, into target data 43 based on the target points 41 after conversion, that is, the target degrees of belonging 42, and the center of gravity C of each cluster d.

[0179] As shown in FIG. 4C, the target data 43 is data x consisting of multiple variables 31b, similar to the input data 31a. nml In the above-mentioned specific example, the target data 43 is a plurality of time-series data measured at different locations.

[0180] The target data 43 is G(∈R M×L ), and the target attribution 42 is P'(∈R D ) Then, the conversion in step S53 can be performed based on, for example, the following formula:

[0181]

number

[0182] As shown in the above formula, the target data 43 can be calculated through a weighted average of the centroid C, with the target degree of membership 42 as the weight.

[0183] In the following step S55, the CPU 3 outputs the target data 43. The target data 43 is stored in a storage unit such as the SSD 9, or visualized on a display unit such as the display 11.

[0184] <3. Other processing> -Extending the domain of the membership probability P- The upper-level belonging probability P is basically defined to be a value between 0 and 1, but the definition may be expanded.

[0185] This expansion can be performed using each input data 31a before soft clustering, the belonging probability P obtained by soft clustering as described above, and the centroid C obtained for each cluster d. The expanded belonging probability P nd can be used in each of the processes described above.

[0186] Specifically, the CPU 3 assigns a weighting coefficient a for each sample n and cluster d. nd Given the corresponding centroid C dml The weighted average of each data x nml Approximation data x nml ' gives.

[0187]

number

[0188] The CPU 3 provides the approximation for all samples n and calculates the approximate data x nml ' and the original data x nml The objective function is the distance between ndThe optimization problem is solved using the values ​​of as design variables. The distance used in the objective function may be calculated for each sample by using the norm of each matrix element, such as the Frobenius norm, or, when an alignment matrix is ​​used, the distance function using the DTW method as described above may be used.

[0189] Then, CPU3 calculates the membership probability P nd and weighting coefficient a nd By ensembling (e.g., averaging over each sample n), the expanded membership probability P nd is obtained.

[0190] In this ensemble, the "extended membership probability P nd If we do not use ensemble, we can impose a constraint that the sum of the weighting coefficients a nd In the latter case, the membership probability P nd Instead of the weighting factor a nd will be used.

[0191] As mentioned above, if the constraints on the sum are satisfied, the extended membership probability P nd or weighting factor a nd The value of may be negative or may exceed 1. As an example, consider the case where D=2.

[0192] In this case, if we use the usual definition, the probability of belonging is P n1 is the x-axis, and the probability of belonging is P n2 In the coordinate plane with y-axis at (P n1 ,P n2 ) combination is allowed. The first probability of belonging is P n1 and the second membership probability P n2 Both are in the real number range between 0 and 1 inclusive.

[0193] On the other hand, as mentioned above, the expanded membership probability P nd16, the point (P n1 ,P n2 ) combination is also allowed. As shown in the figure, the first probability of belonging P n1 The maximum value of P n1_Max exceeds 1 and its minimum value P n1_Min Similarly, the second membership probability P n2 The maximum value of P n2_Max exceeds 1 and its minimum value P n2_Min These trends are reflected by the weighting coefficient a nd The same is true for the value of

[0194] In this way, the CPU 3 according to this embodiment can expand the belonging probability P to a range that allows negative values ​​and values ​​exceeding 1, based on the input data set 31 and the centroid data set 33.

[0195] <4. Significance of data conversion method> As described above, the CPU 3 generates D-dimensional data by soft clustering, and then reduces the dimension of the D-dimensional data to D-1-dimensional data by principal component analysis (see character 4A). As a result, as shown in FIG. 11, it is possible to reduce the dimension of each belonging probability P by principal component analysis while maintaining the soft-clustered state.

[0196] Here, the sum of the belonging probabilities P obtained by soft clustering for each sample (input data 31a) n is 1 (=100%). In other words, the belonging degree dataset 32 ​​corresponds to a hyperplane (D-1 dimensional plane) in a D dimensional space. The belonging degree dataset 32 ​​can be considered to be essentially a collection of D-1 dimensional data.

[0197] Therefore, even if the dimension is reduced to D-1 by principal component analysis, the hyperplane is merely rotated so as to align with the D-1 dimensional plane. Therefore, for example, by using the inverse matrix of the rotation matrix R, the data structure before the dimension reduction can be restored.

[0198] In this way, according to the embodiment, it is possible to perform clustering involving dimensionality reduction and restore the data structure before dimensionality reduction at the same time.

[0199] Furthermore, as illustrated in Figures 4B and 10, the CPU 3 calculates and outputs the index B based on the difference σ between the centers of gravity C obtained as a by-product of the soft clustering process, rather than the difference between the raw data (input data 31a) that was the subject of the soft clustering process.

[0200] This allows for the extraction of feature quantities S in units of clusters d and variables m, rather than the individual features of the input data 31a, making it possible to perform more systematic analysis. This more systematic analysis contributes to the exploration of engineering phenomena, intellectual discovery, and the like. Furthermore, extraction in units of clusters d can provide a more easily recognizable representation when visualizing the extraction results.

[0201] 12 and 13, by associating index B with center of gravity C or index B with input data 31a, it is possible to visualize features and events that appear in units of center of gravity C (i.e., cluster d), or to visualize features and events that appear individually in units of input data 31a (i.e., sample n). This contributes to realizing visualization with excellent visibility.

[0202] As shown in Figs. 11 and 14, each principal component score Q nd This makes it possible to directly analyze the contribution of each variable m to the principal component space Sp1. This allows analysis to be performed from various perspectives, while also increasing the visualization options in the principal component space Sp1. This contributes to the realization of visualizations with excellent visibility, and ultimately to analysis based on the visualization content.

[0203] As shown in Figure 14, for each input data before soft clustering, each principal component score Q nd This allows us to analyze the contribution of the principal component to the analysis. This makes it possible to perform analysis from various perspectives, while also increasing the options for visualization in the principal component space Sp1. This contributes to the realization of visualization with excellent visibility, and ultimately to analysis based on the visualization content.

[0204] In addition, by visualizing each variable axis Ax as shown in Figure 11, it is possible to visualize the variable m (or the physical quantity related to the variable) corresponding to any feature S and the principal component score Q nd This allows visualization of the correlation between and , which contributes to the realization of visualization with excellent visibility and, in turn, to analysis based on the visualized content.

[0205] 4C and 15, any target point 41 specified in the principal component space Sp1 can be converted into target data 43 in the data space to which the input data 31a belongs and output. This allows the user to obtain data in the same format as the input data 31a simply by finding the desired target point 41 in the principal component space Sp1. This enables analysis based on the principal component space Sp1.

[0206] 4C and 15, etc., make good use of the fact that the data structure can be restored, as described above. Furthermore, by using it in combination with the variable axis Ax as shown in FIG. 11, it becomes convenient for searching for an arbitrary target point 41, and analysis from a different perspective than before becomes possible.

[0207] Furthermore, as mentioned above, by extending the domain of the membership probability P to negative values, it becomes possible to perform analysis with greater flexibility, which is advantageous for analysis based on the principal component space Sp1 and for restoring the data structure from the principal component space Sp1.

[0208] 14, by using time-series data for each input data 31, it is possible to incorporate the influence of the passage of time, such as the change from the peak of the vertical displacement, in various analyses. This makes it possible to visualize and analyze from various perspectives.

[0209] Furthermore, by using the c-means method, the belonging probability P and the center of gravity C can be calculated simply by specifying the number of clusters D. This is advantageous for various processes and analyses based on the belonging probability P and the center of gravity C, such as the various visualizations mentioned above.

[0210] <5. Other embodiments> Additionally, although the above embodiment has shown an example in which the data conversion device is configured by one computer 1, the present disclosure is not limited to this example. The data conversion method and data conversion program 23 according to the present disclosure may be executed using multiple computers 1, such as by having a first computer execute some of the processing and a second computer execute the remaining processing. Furthermore, the computer 1 in the present disclosure also includes parallel computers such as supercomputers and PC clusters.

[0211] Furthermore, the screen on which the various visualized information can be displayed is not limited to the display screen on the display 11 of the computer 1. A scatter diagram or the like may be displayed on a screen prepared separately from the computer 1. [Explanation of symbols]

[0212] 1. Computer (data conversion device) 3 CPU (arithmetic unit) 7 RAM (memory section) 9 SSD (storage unit) 11 Display (display unit) 15 Mouse (operation part) 17 Keyboard (operation section) 18 Storage medium 23 Data Conversion Program 31 Input Datasets 31a Input data 31b variable 32 Attribution Dataset 33 Centroid Dataset 34 Principal Component Dataset 35 Rotation matrix data 36 centroid contribution dataset 37 feature dataset 41 Target points (points) 42 Goal Attribution 43 Target Data (Data) C Center of gravity P Membership probability B Indicator S feature σ difference Sp1 principal component space

Claims

1. 1. A data conversion method for converting an input data set consisting of a plurality of input data, each having a plurality of variables, by using a calculation unit of a computer, comprising: the calculation unit performs soft clustering on the input data set to classify each of the input data sets into D clusters (D is a natural number equal to or greater than 2), and outputs a centroid data set including centroids of the D clusters and a membership data set including D-dimensional data indicating a probability of belonging to each of the D clusters for each of the input data sets; The calculation unit performs principal component analysis on the membership dataset, thereby outputting a principal component dataset in which the D-dimensional data has been reduced to D-1-dimensional data. A data conversion method comprising:

2. 2. The data conversion method according to claim 1, the centroid is given for each variable constituting the input data, the calculation unit calculates, for each variable, a difference between centers of gravity belonging to different clusters among the centers of gravity of each of the D clusters; The calculation unit outputs, based on the difference, an index characterizing a difference between the different clusters as a centroid contribution data set including the index for each cluster and for each variable. A data conversion method comprising:

3. 3. The data conversion method according to claim 2, The calculation unit visualizes the index in association with the centroid dataset or the input dataset. A data conversion method comprising:

4. 3. The data conversion method according to claim 2, the calculation unit acquires a rotation matrix from a D-dimensional space to which the membership dataset belongs to a principal component space to which the data after the principal component analysis belongs, The calculation unit converts the index by the rotation matrix, and outputs the index as a feature data set in which the dimension of the index is reduced from the D-dimensional data to D-1-dimensional data and which includes the feature amount for each variable. A data conversion method comprising:

5. 5. The data conversion method according to claim 4, The computing unit visualizes the feature amounts by associating them with the input data set for each of the variables. A data conversion method comprising:

6. 5. The data conversion method according to claim 4, The calculation unit visualizes the variable axes corresponding to the feature quantities in association with the principal component axes in the principal component data set. A data conversion method comprising:

7. 2. The data conversion method according to claim 1, the calculation unit acquires a rotation matrix from a D-dimensional space to which the membership dataset belongs to a principal component space to which the data after the principal component analysis belongs, the calculation unit accepts designation of an arbitrary point in the principal component space, the calculation unit transforms the points from the principal component space to points in the D-dimensional space based on the rotation matrix; The calculation unit converts the converted points into data configured by the plurality of variables based on the probability of belonging to each of the D clusters and the center of gravity of each cluster assigned to each of the variables, and outputs the converted points. A data conversion method comprising:

8. 7. The data conversion method according to claim 6, The calculation unit expands the membership probability to a range that allows negative values ​​and values ​​greater than 1 based on the input data set and the centroid data set. A data conversion method comprising:

9. 9. The data conversion method according to claim 2, the variables and the centroids are time-series data in which a plurality of numerical values ​​are arranged in a time series, The index is calculated for each numerical value constituting the time series data. A data conversion method comprising:

10. 2. The data conversion method according to claim 1, The calculation unit performs the soft clustering by using a c-means method. A data conversion method comprising:

11. 1. A data conversion device that converts an input data set composed of a plurality of input data each having a plurality of variables by using a calculation unit of a computer, comprising: a means for performing soft clustering on the input data set to classify each of the input data sets into D clusters (D is a natural number equal to or greater than 2), and outputting a centroid data set including the centroids of the D clusters and a membership data set including D-dimensional data indicating the probability of each of the input data sets belonging to each of the D clusters; means for performing principal component analysis on the membership dataset to output a principal component dataset in which the D-dimensional data has been reduced to D-1-dimensional data; A data conversion device characterized by:

12. A data conversion program that, when executed by a calculation unit of a computer, converts an input data set that is made up of a plurality of input data, each of which has a plurality of variables, comprising: The computer, a process in which the calculation unit performs soft clustering on the input data set to classify each of the input data sets into D clusters (D is a natural number equal to or greater than 2), and outputs a centroid data set including the centroids of the D clusters, and a membership data set including D-dimensional data indicating the probability of each of the input data sets belonging to each of the D clusters; the calculation unit executes a process of performing principal component analysis on the membership dataset, thereby outputting a principal component dataset in which the D-dimensional data has been reduced to D-1-dimensional data. A data conversion program characterized by:

13. The data conversion program according to claim 12 is stored. A computer-readable storage medium comprising:

Images