JP4188181B2 - Multivariate data selection device and multivariate data selection program - Google Patents

Description

  The present invention relates to a multivariate data selection device and a multivariate data selection program for selecting a variable reflecting a data structure from large-scale data.

  Conventionally, in variable selection aiming at knowledge extraction from large-scale data, the method of McCabe (1984) (FIG. 13) for specifying an important variable by considering the correlation of the variables (for example, Non-Patent Document 1) ), After using the dimension compression method represented by principal component analysis, the method of Krzanowski (1987) (FIG. 14) for selecting a variable by quantifying the variation of the sample before and after selecting the variable. It has been proposed (for example, Non-Patent Document 2).

FIG. 15 is a flowchart for explaining the operation by the Krzanowski method. First, processing target data X described in a file or the like and parameters (selection variable number q and principal component number r) are input from an input device (S10). Next, principal component analysis is applied to X to calculate a principal component score, which is set as Y (S12). Next, determine the similarity M ² and Z generated by the Y and internally obtaining a combination of variable corresponding thereto (S14). Next, the variable corresponding to the variable combination obtained in step S14 is output as the best selected variable (S16).

  Next, FIG. 16 is a flowchart for explaining the detailed operation of step S14 described above. First, all pCq combinations of variables are obtained from the selected variable number q and the total variable number p (S20). For example, when q = 2 and there are variables x1, x2, and x3, a combination of (x1, x2) (x2, x3) (x3, x1) is obtained. Next, one combination is sequentially extracted from the result of Step 20, and principal component analysis is applied to the submatrix X˜ configured by one of the combinations, thereby obtaining principal component scores in descending order of eigenvalues. This is calculated and set as Z (S22).

Next, a procrustes criterion M ² (see note 1) is calculated from Y and Z, and the value is used as a similarity, and stored, for example, so that the value is not overwritten in the array (S24). Then, for all combinations of the variables obtained in step S20, it is checked whether to calculate the Procrustes reference M ² (S26). If the similarity is not calculated for all combinations, the process returns to step S22 and the above-described processing is repeated. On the other hand, when the similarity is calculated for all the combinations, the value having the highest similarity among the M ² stored in step S24 is set as the final similarity, which is similar to the corresponding combination. The degree is output (S28).

Note 1: M ² = tr (YY ^t + ZZ ^t −2D)
D is a matrix in which singular values are arranged diagonally. Here, in order to match the dimensionality of Y and Z, a principal component score corresponding to a low principal component is discarded among q principal component scores that can be originally extracted.
G. P. McCabe, “Principal Variables,” Technologies, vol. 26, pp. 137-144, 1984. W. J. et al. Krzanowski. “Selection of variables to preserve multivariate data structure, using principal components,“ Applied Statistics, vol. 36, pp. 22-33, 1987.

  However, in the conventional McCabe method, attention is paid only to individual variables, and effective variables are not selected when viewed as variables as a whole. In addition, in the Krzanowski method, a variable selection method that takes into account the correlation of data and focuses on the subspace spanned by the data has also been proposed. When comparing this subspace and the variable group of selection candidates, In order to match the dimensions, it is necessary to reduce the dimensions, and there is a problem in that information of data included in the variable group of selection candidates is damaged.

  Therefore, an object of the present invention is to provide a multivariate data selection device and a multivariate data selection program that can select a variable that reflects the data structure of the entire variable.

For the purposes achieved, the present invention includes a process target data, input means for inputting the selected variables count and number of principal components as parameters of the processing target data, the main to the processing target data input by said input means Eigenvalues and eigenvectors are obtained using a component analysis technique, the number of principal components is extracted in order from eigenvectors with the highest eigenvalues, base calculation means for constructing a base vector of the processing target data, and all of the selected variable numbers from the processing target data A variable combination is extracted, one combination is sequentially extracted from the combination of the variables, and orthonormal basis constructing means each constituting an orthonormal basis vector; the basis vector calculated by the basis calculating means; and the orthonormal basis constructing means The canonical angle of the orthonormal vector generated in step 1 is sequentially calculated and stored for the orthonormal prescribed vector. Outputs the similarity calculation means, as a combination of variables to be selected the variable combinations similarity to (angle minimum) the greatest constitutes an orthonormal vector of canonical angle calculated by the similarity calculation means And an output means .

Further, the present invention provides a computer with an input means for inputting processing target data, a selected variable number and the number of principal components as parameters of the processing target data, and a principal component analysis for the processing target data input by the input means. The eigenvalues and eigenvectors are obtained using a technique, the principal component numbers are extracted in order from the eigenvectors with the highest eigenvalues, basis calculation means for constructing the basis vectors of the processing target data, and all the variable combinations of the selected variable numbers from the processing target data. Extracted, sequentially extracted one combination from the combination of variables, and generated by the orthonormal basis constructing means that constitutes orthonormal basis vectors, the basis vectors calculated by the basis calculating means, and the orthonormal basis constructing means canonical angles of the orthonormal basis vectors partial sequentially calculated and stored for the class of orthonormal vectors Degree calculating means, output means for outputting as a combination of variables to be selected the variable combinations similarity to (angle minimum) the greatest constitutes an orthonormal vector of the similarity canonical angles calculated by the calculating means , A multivariate data selection program for functioning as

  According to the first aspect of the present invention, the basis calculation unit extracts several eigenvectors having high eigenvalues in order from the processing target data input from the input unit using a predetermined basis derivation method, A basis vector of data is calculated, a similarity calculation unit obtains a similarity between the basis vector and an orthonormal basis vector generated internally, a combination of variables corresponding to the similarity is obtained, and an output unit Since the variable corresponding to the combination of variables is output as the best selected variable, it is possible to select a variable reflecting the data structure of the entire variable, and when obtaining the basis vector for the original data In addition, by changing the basis vector calculation method (for example, discriminant criterion), it is possible to select a variable according to the purpose. Through out (e.g. scatter plot), the advantage is obtained that it is possible to facilitate the interpretation of the results.

  According to the invention of claim 2, in the similarity calculation means, the variable combination calculation means obtains all combinations of variables from the selected variable numbers and the total variable numbers input as parameters of the data, The orthonormal basis constructing means sequentially extracts one combination from the combination of variables to form an orthonormal basis, and the angle calculating means sets the angle between the orthonormal basis and the base for all the combinations of variables. Since the value is used as the similarity, it is possible to select a variable that reflects the data structure of the entire variable, and when obtaining the basis vector for the original data, By changing the calculation method (eg discriminant criterion), it is possible to select the variable according to the purpose, and hence the effective variable set extraction (eg scatter diagram) Through, the advantage is obtained that it is possible to facilitate the interpretation of the results.

  According to the invention of claim 3, a value having the highest similarity among the angles calculated by the angle calculation means by the output means is set as a final similarity, and a combination corresponding thereto. Since the similarity is output, it is possible to select a variable reflecting the data structure of the entire variable, and change the calculation method of the base vector when obtaining the base vector for the original data ( For example, it is possible to select a variable according to the purpose, and therefore, it is possible to facilitate the interpretation of the result through effective variable set extraction (for example, a scatter diagram).

  According to the invention described in claim 4, using the step of inputting the data to be processed and a predetermined basis derivation method, several eigenvectors having high eigenvalues are extracted in order, and the basis vector of the data is obtained. A step of calculating, a step of obtaining a similarity between the basis vector and an orthonormal basis vector generated internally, a step of obtaining a combination of variables corresponding to the similarity, and a variable corresponding to the combination of the variables. Since the computer executes the step of outputting as the best selected variable, it is possible to select a variable that reflects the data structure of the entire variable, and when obtaining the basis vector for the original data, By changing the basis vector calculation method (for example, discriminant criterion), it is possible to select a variable according to the purpose. Through variable set extraction (e.g. scatter plot), the advantage is obtained that it is possible to facilitate the interpretation of the results.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

A. Configuration of Embodiment FIG. 1 is a block diagram showing a configuration of a multivariate data selection apparatus according to an embodiment of the present invention. In the figure, an input unit 110 inputs data X (nxp matrix) to be processed, a selected variable number q, and a principal component number r. The calculation unit 120 performs various processes, and selects an optimal variable according to the set base. The output unit 130 outputs the processed data matrix.

B. Principle of Multivariate Data Selection Method According to the Present Invention FIG. 2 is a conceptual diagram for explaining the principle of the multivariate data selection method of the present invention.
That is, to quantify the similarity subspaces each other orthonormal basis X_ variables selected before subspace (eigenvectors) of the data X Y ^lambda and random selection candidate X~ numerically by canonical angles, with the maximum similarity Select a combination of variables as an effective variable when viewed as a whole variable. Thereby, it is possible to prevent the loss of information of data and to select a variable that more reflects the data structure. Details will be described later in the operation of the embodiment.

C. Operation of Embodiment Next, the operation of the above-described embodiment will be described. Here, FIG. 3 is a flowchart for explaining the operation of the multivariate data selection apparatus according to the present embodiment. FIG. 4 is a conceptual diagram for explaining the operation of the multivariate data selection apparatus according to the present embodiment. First, data X to be processed described in a file or the like and parameters (a selected variable number q and a main component number r) are input from the input unit 110 (S40). An example of input data is shown in Equation 1.

Then, because of the underlying derivation of data X, using a base derivation of principal component analysis and discriminant analysis, extraction turn the r eigenvectors with high eigenvalues, as a base Y λ ^(S42). An example of the basis is shown in Equation 2.

Next, the similarity λ max between the orthonormal basis X_ composed of Y ^λ and the selected variable combination X˜ is obtained, and the corresponding variable combination X ^λ is obtained (S44). Then, the variable combination corresponding to the variable combination X ^{λ — having} the largest λmax is output as the best selected variable (S46).

Next, FIG. 5 is a flowchart for explaining the detailed operation of steps S44 and S46 described above. FIG. 6 is a conceptual diagram for explaining detailed operations of steps S44 and S46. First, all pCq combinations of variables are obtained from the selected variable number q and the total variable number p (S50, see FIG. 6A). For example, when q = 2 and there are variables a, b, and c, a combination of (a, b), (b, c), and (c, a) is obtained. Next, one combination is sequentially extracted from the ending of step S50 to form an orthonormal basis X_ (see S52, FIG. 6B).

Next, the maximum eigenvalue λmax of the angle λ between the subspaces is calculated from the orthonormal basis X_ and the basis Y ^λ obtained in step S42, and the value is used as a similarity, for example, so that the value is not overwritten in the array Save it (S54, see FIG. 6C). Next, it is checked whether the maximum eigenvalue λmax of the angle has been calculated for all the variable combinations obtained in step S50 (S56). If the similarity is not calculated for all combinations, the process returns to step S52 and the above-described processing is repeated. On the other hand, when the similarity is calculated for all the combinations, the value having the highest similarity among the maximum eigenvalues λmax of the angles stored in step S54 is set as the final similarity and corresponds to it. The combination and the similarity are output (S58, see FIGS. 6D and 6E).

D. Specific Example Next, a specific example of the multivariate data selection process performed using the multivariate data selection apparatus according to the present embodiment will be described. In this specific example, data obtained by measuring the physical characteristics of a feather ant are used. The data size was 40 samples and 19 variables. FIG. 7 is a table showing the variables selected by the multivariate data selection method according to this embodiment. In the figure, the variable indicated by ○ is selected. The variable No. Since 18 is category data, the data having a wrinkle is coded as “1” and the data having no wrinkle is coded as “0”. Further, the variable number q to be selected was set to 4, and the number r of main components to be used was set to 2.

  Here, the multivariate data selection method of the present invention and the conventional method are applied to the data shown in FIG. From the viewpoint of all the original feature approximations through the scatter diagram with the first principal component (corresponding to PC1 in FIG. 7) and the second principal component (corresponding to PC2 in FIG. 7) using the variables selected by the respective methods. Compare the effects of variable selection. 8, 9, 11, and 12 described below, the first principal component corresponds to “PC1” and the second principal component corresponds to “PC2”.

  Here, FIG. 8 is a scatter diagram using all variables. FIG. 9 is a scatter diagram using the variables having the highest importance among the variables selected by the multivariate data selection method according to the present embodiment. As shown in FIG. 9, it can be seen that the cluster structure is preserved and the positional relationship is not significantly different without using all variables.

  FIG. 10 is a table showing the variables selected by the conventional method. In the figure, the variable indicated by ○ is selected. FIG. 11 is a scatter diagram using the variables selected by the conventional method (MaCube (1984)), and FIG. 12 is a scatter diagram using the variables selected by the conventional method (Krzanowski (1987)). is there. As shown in FIG. 11, it can be seen that the cluster structure is broken in the conventional method (MaCabe (1984)). Also, as shown in FIG. 12, it can be seen that the original information is not sufficiently reflected in the distribution distance in the conventional method (Krzanowski (1987)).

  In the above-described embodiment, the function of the calculation unit 120 is realized by executing a program stored in a storage unit (not shown). The storage unit is configured by a hard disk device, a magneto-optical disk device, a nonvolatile memory such as a flash memory, a volatile memory such as a RAM (Random Access Memory), or a combination thereof. Further, the storage unit is a fixed time such as a volatile memory (RAM) in a computer system serving as a server or a client when a program is transmitted via a network such as the Internet or a communication line such as a telephone line. Includes those holding programs.

  The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information such as a network such as the Internet or a communication line such as a telephone line. The program may be for realizing a part of the above-described processing. Furthermore, what can implement | achieve the process mentioned above in combination with the program already recorded on the calculating part 120, what is called a difference file (difference program) may be sufficient.

  The embodiment of the present invention has been described in detail with reference to the drawings. However, the specific configuration is not limited to the above-described embodiment, and includes designs and the like that do not depart from the gist of the present invention.

It is a block diagram which shows the structure of the multivariate data selection apparatus by embodiment of this invention. It is a conceptual diagram for demonstrating the principle of the multivariate data selection method of this invention. It is a flowchart for demonstrating operation | movement of the multivariate data selection apparatus by this embodiment. It is a conceptual diagram for demonstrating operation | movement of the multivariate data selection apparatus by this embodiment. It is a flowchart for demonstrating the partial detailed operation | movement of this embodiment. It is a conceptual diagram for demonstrating the partial detailed operation | movement of this embodiment. It is a table | surface figure which shows the variable selected by the multivariate data selection method by this embodiment. It is a scatter diagram using all the variables. It is a scatter diagram using the variable with the highest importance among the variables selected by the multivariate data selection method according to the present embodiment. It is a table | surface figure which shows the variable selected by the conventional method. It is a scatter diagram using the variable selected by the conventional method (MaCabe (1984)). It is a scatter diagram using the variable selected by the conventional method (Krzanowski (1987)). It is a conceptual diagram which shows the principle of the conventional method (McCabe (1984)). It is a conceptual diagram which shows the principle of the conventional method (Krzanowski (1987)). It is a flowchart for demonstrating the operation | movement by a Krzanowski method. It is a flowchart for demonstrating in detail some operation | movement of a Krzanowski method.

Explanation of symbols

110 Input unit (input means)
120 arithmetic unit (base calculation means, similarity calculation means, variable combination calculation means, orthonormal basis construction means, angle calculation means)
130 Output unit (output means)

Claims (2)

A multivariate selection device including an input unit, a calculation unit, and an output unit,
The input unit is
an input means for inputting processing target data consisting of an n × p matrix (n sample data indicated by p variables) and a selected variable number q and a selected principal component number r as parameters of the processing target data ;
The computing unit is
Wherein the processed data inputted to principal component analysis with input means obtains eigenvectors of p × p matrix corresponding to p eigenvalues and eigenvalues, wherein the selected number of principal components descending order of the eigenvalues of the determined eigenvalues ( r) eigenvalues and basis calculation means for calculating a corresponding eigenvector as a basis vector (p × r matrix) of the processing target data;
All (pCq) variable combinations are extracted from the total variable number p and the selected variable number q of the processing target data input by the input unit, and the row direction is the extraction source of the variable combination. Is a p × q matrix that indicates q variable types extracted by the variable combination in the column direction, and the other elements are the same in the row and column variable types. Orthonormal basis constructing means for constructing pCq number of p × q matrices as many as the number of the variable combinations represented by 0 as pCq orthonormal basis vectors;
A canonical angle between the basis vector calculated by the basis calculation means and one orthonormal basis vector sequentially selected from the pCq orthonormal basis vectors configured by the orthonormal basis configuration means is calculated and stored sequentially . A canonical angle calculation means ,
The output unit is
An output means for outputting the combination of the variables constituting the orthonormal basis vector having the smallest angle among the canonical angles calculated and stored by the canonical angle calculating means ;
A multivariate data selection device characterized by comprising: In a computer composed of an input unit, a calculation unit, and an output unit,
In the input part of the computer,
input means for inputting processing target data consisting of an n × p matrix (n sample data indicated by p variables) and a selected variable number q and a selected principal component number r as parameters of the processing target data ;
In the computing unit of the computer,
Wherein the processed data inputted to principal component analysis with input means obtains eigenvectors of p × p matrix corresponding to p eigenvalues and eigenvalues, wherein the selected number of principal components descending order of the eigenvalues of the determined eigenvalues ( r) eigenvalues and basis calculation means for calculating a corresponding eigenvector as a basis vector (p × r matrix) of the processing target data;
All (pCq) variable combinations are extracted from the total variable number p and the selected variable number q of the processing target data input by the input unit, and the row direction is the extraction source of the variable combination. Is a p × q matrix that indicates q variable types extracted by the variable combination in the column direction, and the other elements are the same in the row and column variable types. Orthonormal basis constructing means for constructing pCq number of p × q matrices corresponding to the number of the variable combinations indicated by 0 as pCq orthonormal basis vectors,
A canonical angle between the basis vector calculated by the basis calculation means and one orthonormal basis vector sequentially selected from the pCq orthonormal basis vectors configured by the orthonormal basis configuration means is calculated and stored sequentially . Canonical angle calculation means ,
In the output part of the computer,
An output means for outputting the combination of the variables constituting the orthonormal basis vector having the smallest angle among the canonical angles calculated and stored by the canonical angle calculation means;
Program to function as.

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