CN109034270A - A kind of visualization feature selection method based on the classification Non-negative Matrix Factorization of failure two - Google Patents

Abstract

A visual feature selection method based on non-negative matrix decomposition of fault binary classification. First, the multi-classification problem is divided into multiple binary classification problems according to the arrangement and combination. Graph expression, and finally use the salience expression principle of the heat map to select effective classification features, and extract the sensitive features of the entire data set through the classification features; While performing dimensionality reduction, good classification performance of low-dimensional feature subsets is guaranteed.

Description

A visual feature selection method based on fault binary classification non-negative matrix factorization

technical field

The invention belongs to the technical field of mechanical equipment state detection and fault diagnosis, and in particular relates to a visual feature selection method based on fault binary classification non-negative matrix decomposition.

Background technique

As the complexity and level of integration of electromechanical systems continue to increase, so does the risk of equipment failure during operation. In order to accurately identify the faults initiated and evolved during the operation of the electromechanical system, and to diagnose and deal with abnormal components in a timely manner, condition monitoring and fault diagnosis become very necessary. With the continuous advancement of information acquisition technology, more and more feature quantities about system status and operating parameters can be obtained, including redundant and irrelevant feature information, which brings great challenges to subsequent diagnosis and identification. Effective feature selection and extraction work on high-dimensional data is required. In addition to the traditional dimension reduction method, the Non-negative Matrix Factorization (NMF) method can obtain the low-rank approximation of the original feature data matrix, and the decomposition results have better interpretability and physical meaning. The relevant decomposition matrix can realize the dimensionality reduction of data features, and has been popularized and applied in the field of monitoring and diagnosis.

However, in the current eigenanalysis method based on non-negative matrix decomposition, the direct analysis of the basis matrix or coefficient matrix of the original multi-type fault sample matrix decomposition is used, and the algorithm is the center, and the selection process usually lacks human participation, resulting in the selection of The process is not transparent and intuitive enough, and the interpretability of the selection results is not strong, which limits the effect of feature analysis and selection.

Contents of the invention

In order to overcome the shortcomings of the above-mentioned prior art, the object of the present invention is to provide a visual feature selection method based on non-negative matrix decomposition of fault binary classification, which combines the physical meaning of non-negative matrix decomposition results and the significant expression advantages of heat maps, It makes feature selection intuitive and visual, and ensures the classification accuracy of the selected feature subset.

In order to achieve the above object, the technical scheme adopted in the present invention is:

A visual feature selection method based on fault binary classification non-negative matrix decomposition, comprising the following steps:

1) Extract the data set V _m×n to be processed, the row m of the data set represents the sample, and the column n represents the feature;

2) Perform non-negativeization and normalization processing on the data set V _m×n ,

In the formula: i=1,2,...,m; j=1,2,...,n, maxV _ij is the maximum value of column vector V _j ; minV _kj is the minimum value of column vector V _j ;

3) The original multi-fault classification problem is divided into multiple binary classification problems according to the arrangement and combination. Assuming that V _m×n contains N types of samples, the feature set corresponding to each divided binary classification problem is expressed as P _i , where

4) For each non-negative feature set Use the least squares iterative algorithm to decompose, that is, P _i =W _i H _i ;

Randomly initialize W _i and H _i , the low-dimensional embedding dimension r _i is preferably selected to be the same as the number of sample categories, and the base matrix W _i and coefficient matrix H _i are obtained by non-negative matrix decomposition. The iteration rules are as follows:

In the formula: Wi is the base matrix obtained by non-negative matrix decomposition of feature set P _i , Represents the transpose of the base matrix W _i , and H _i is the coefficient matrix obtained by the non-negative matrix decomposition of the feature set P _i , Represents the transpose of the coefficient matrix H _i ;

5) Visualize the base matrix W _i and the coefficient matrix H _i in a heat map, the rows of the base matrix W _i correspond to the samples, and the columns of the coefficient matrix H _i correspond to the original features;

6) Observe the feature clustering of the base matrix W _i , if the two types of samples can be observed to be clearly separated in one column of the base matrix W _i , then proceed to step 7), otherwise re-select the low-dimensional embedding dimension r _i , and return to step 4 );

7) Use the principle of salience expression to select the classification feature F _i in the heat map, and control the number of classification features to 1 by adjusting the threshold of the heat map;

8) Perform a union operation on the classification features F _i obtained for all binary classification problems to obtain the final classification feature set F,

The beneficial effects of the present invention are: the method of the present invention can realize the mutual cooperation and complementary advantages of the computer and the human, the selected result can be interpreted strongly, and the original high-dimensional original features are reduced in dimension while ensuring the low-dimensional feature subset. Good classification performance.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention.

Fig. 2 is a visualization effect diagram of the heat map of the non-negative matrix decomposition result of the data set P ₁ (the first and second types of sample sets) in the embodiment.

Fig. 3 is a visualization effect diagram of the heat map of the non-negative matrix decomposition result of the data set P ₂ (the first and third types of sample sets) in the embodiment.

Fig. 4 is a visualization effect diagram of the heat map of the non-negative matrix decomposition result of the data set P ₃ (the second and third types of sample sets) in the embodiment.

Fig. 5 is a three-dimensional visualization effect diagram of features 1, 7 and 12 of the wine dataset in the embodiment.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and examples. This implementation case is developed for the Wine data set in the UCI data set. The Wine data set comes from the chemical analysis results of three different varieties of wine. The analysis has determined 13 of the three wines. The specific content of ingredients, the Wine dataset contains three types of data, a total of 178 samples, 13 kinds of characteristic attributes (components), the number of samples for each category is: 59 (category 1), 71 (category 2), 48 (category 3 ), this embodiment performs feature selection on these 13 features, and selects features with good classification performance.

Referring to Figure 1, a visual feature selection method based on fault binary classification non-negative matrix decomposition, including the following steps:

1) extract the data set V _{m * n} to be processed, the row m of the data set represents the sample, and the column n represents the feature, and the present embodiment adopts the Wine data set;

2) Perform non-negativeization and normalization processing on the data set V _m×n ,

In the formula: i=1,2,...,m; j=1,2,...,n, maxV _ij is the maximum value of column vector V _j ; minV _kj is the minimum value of column vector V _j ;

3) The original multi-fault classification problem is divided into multiple binary classification problems according to the arrangement and combination. Assuming that V _m×n contains N types of samples, the feature set corresponding to each divided binary classification problem is expressed as P _i , where In this embodiment, the Wine data set is divided into three binary classification problems according to the principle of permutation and combination, which are P ₁ (the first and second types of sample sets), P ₂ (the first and third types of sample sets), P ₃ (the second and third types of sample sets), and P 3 (the second and third types of sample sets). sample collection);

4) For each non-negative feature set Use the least squares iterative algorithm to decompose, that is, P _i =W _i H _i ;

Randomly initialize W _i and H _i , the low-dimensional embedding dimension r _i is preferably selected to be the same as the number of sample categories, and the base matrix W _i and coefficient matrix H _i are obtained by non-negative matrix decomposition. The iteration rules are as follows:

In the formula: W _i is the basis matrix obtained by non-negative matrix decomposition of feature set P _i , Represents the transpose of the base matrix W _i , and H _i is the coefficient matrix obtained by the non-negative matrix decomposition of the feature set P _i , Represents the transpose of the coefficient matrix H _i ;

5) Visualize the base matrix W _i and the coefficient matrix H _i in a heat map, the rows of the base matrix W _i correspond to the samples, and the columns of the coefficient matrix H _i correspond to the original features;

6) Observe the feature clustering of the base matrix W _i , if the two types of samples can be observed to be clearly separated in one column of the base matrix W _i , as shown in Figure 2, then proceed to step 7), otherwise re-select the low-dimensional embedding dimension r _i , return to step 4);

From the perspective of clustering, the feature set of the binary classification problem should essentially contain only two types of features, that is, the features that can distinguish and cannot distinguish the binary classification problem, and other features can be obtained by combining these two types of essential features; therefore, this implementation For example, when performing non-negative matrix decomposition on P ₁ , P ₂ , and P ₃ , the low-dimensional embedding dimension r is preferred to 2, and the visual representation of the final decomposition results is shown in Figures 2, 3, and 4;

7) The principle of significant expression is adopted in the heat map, that is, according to the matrix multiplication rule, the large number × large number will still be a large number, which is distinguished from the small value in the heat map; through the coefficient matrix H _i corresponding to the large number area The classification feature F _i is selected from the original features, and the number of classification features is controlled by adjusting the threshold of the heat map. Usually, the number of control features is 1;

8) Perform a union operation on the classification features F _i obtained for all binary classification problems to obtain the final classification feature set F,

In this embodiment, the principle of salience expression of the heat map is used to sequentially select the classification features of the decomposition results of P ₁ , P ₂ , and P ₃ ; by adjusting the display threshold of the heat map, the number of classification features selected for each binary classification problem is controlled. If the number is 1, the final selected classification features can be known from the coefficient matrix H, which are feature 1, feature 7 and feature 12 in turn, and the classification feature set is obtained after union of them as {1, 7, 12}.

This embodiment extracts the 1st dimension, the 7th dimension and the 12th dimension feature in the wine data set to draw a three-dimensional visualization effect diagram of the data set, as shown in Figure 5, as can be seen from this figure, the wines of three different varieties using the method of the present invention It can be well distinguished. Under the KNN classifier, the classification rate of subset F reaches 94.94%.

Through the above application description, the method of the present invention can make the feature selection become intuitive and vivid, the result of the selection can be interpreted strongly, and the classification accuracy of the selected feature subset can be guaranteed, which can help solve the high-level problem of complex electromechanical system monitoring and fault diagnosis. dimensional data analysis to improve the efficiency and accuracy of fault diagnosis.

Claims (1)

1. A visual feature selection method based on fault binary classification non-negative matrix decomposition, is characterized in that, comprises the following steps: 1) Extract the data set V _m×n to be processed, the row m of the data set represents the sample, and the column n represents the feature; 2) Perform non-negativeization and normalization processing on the data set V _m×n , In the formula: i=1,2,...,m; j=1,2,...,n, maxV _ij is the maximum value of column vector V _j ; minV _kj is the minimum value of column vector V _j ; 3) The original multi-fault classification problem is divided into multiple binary classification problems according to the arrangement and combination. Assuming that V _m×n contains N types of samples, the feature set corresponding to each divided binary classification problem is expressed as P _i , where 4) For each non-negative feature set Use the least squares iterative algorithm to decompose, that is, P _i =W _i H _i ; Randomly initialize W _i and H _i , the low-dimensional embedding dimension r _i is preferably selected to be the same as the number of sample categories, and the base matrix W _i and coefficient matrix H _i are obtained by non-negative matrix decomposition. The iteration rules are as follows: In the formula: W _i is the basis matrix obtained by non-negative matrix decomposition of feature set P _i , Represents the transpose of the base matrix W _i , and H _i is the coefficient matrix obtained by the non-negative matrix decomposition of the feature set P _i , Represents the transpose of the coefficient matrix H _i ; 5) Visualize the base matrix W _i and the coefficient matrix H _i in a heat map, the rows of the base matrix W _i correspond to the samples, and the columns of the coefficient matrix H _i correspond to the original features; 6) Observe the feature clustering of the base matrix W _i , if the two types of samples can be observed to be clearly separated in one column of the base matrix W _i , then proceed to step 7), otherwise re-select the low-dimensional embedding dimension r _i , and return to step 4 ); 7) Use the principle of salience expression to select the classification feature F _i in the heat map, and control the number of classification features to 1 by adjusting the threshold of the heat map; 8) Perform a union operation on the classification features F _i obtained for all binary classification problems to obtain the final classification feature set F,