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

A kind of visualization feature selection method based on the classification Non-negative Matrix Factorization of failure two Download PDF

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CN109034270A
CN109034270A CN201810968454.6A CN201810968454A CN109034270A CN 109034270 A CN109034270 A CN 109034270A CN 201810968454 A CN201810968454 A CN 201810968454A CN 109034270 A CN109034270 A CN 109034270A
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matrix
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negative
division
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梁霖
牛奔
刘飞
山磊
何康康
徐光华
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Xian Jiaotong University
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Abstract

A kind of visualization feature selection method based on the classification Non-negative Matrix Factorization of failure two, more classification problems are first divided into multiple two classification problems according to permutation and combination method, then pass through the Non-negative Matrix Factorization of high dimensional feature set, split-matrix is subjected to thermal map expression, the final significant expression principle using thermal map selects effective characteristic of division, by characteristic of division and extract the sensitive features of entire data acquisition system；The present invention can be realized cooperating and having complementary advantages for computer and people, ensure that the good classification performance of low-dimensional character subset while carrying out dimensionality reduction to original higher-dimension primitive character.

Description

A kind of visualization feature selection method based on the classification Non-negative Matrix Factorization of failure two
Technical field
The invention belongs to mechanical equipment state detections and fault diagnosis technology field, and in particular to one kind is divided based on failure two The visualization feature selection method of class Non-negative Matrix Factorization.
Background technique
As the complexity and integrated level of Mechatronic Systems are continuously improved, what equipment broke down in the process of running Risk is also being continuously increased.It is abnormal to occurring in order to accurately identify the failure that Mechatronic Systems is germinated and developed in the process of running Component timely diagnosed and handled, condition monitoring and fault diagnosis just becomes very necessary.And with acquisition of information skill Art is constantly progressive, and the characteristic quantity that can be obtained about system mode and operating parameter is more and more, includes redundancy and nothing Characteristic information is closed, this brings huge challenge for subsequent diagnosis identification, this just needs to carry out effective feature to high dimensional data Selection and extraction work.Other than traditional Dimensionality Reduction method, Non-negative Matrix Factorization (Non-negative Matrix Factorization, NMF) low-rank of the available former characteristic matrix of method approaches, and decomposition result has and can preferably solve The property released and physical significance can be realized the Dimensionality Reduction of data characteristics by split-matrix relevant to feature, in monitoring, diagnosing Field is promoted and applied.
But currently based in the characteristic analysis method of Non-negative Matrix Factorization, using original multiclass fault sample square The basic matrix or coefficient matrix that battle array is decomposed directly are analyzed, and the participation of people is generally deficient of centered on algorithm, in selection course, is caused The process of selection is not transparent intuitive enough, and the result interpretation of selection is not strong, limits the effect of signature analysis and selection.
Summary of the invention
In order to overcome the disadvantages of the above prior art, the object of the present invention is to provide one kind based on failure two classify it is non- The visualization feature selection method that negative matrix decomposes, combines the physical significance of Non-negative Matrix Factorization result and the significant table of thermal map It is superior, so that feature selecting becomes visual pattern, it ensure that the nicety of grading of selected character subset.
In order to achieve the above object, the technical scheme adopted by the invention is that:
A kind of visualization feature selection method based on the classification Non-negative Matrix Factorization of failure two, comprising the following steps:
1) data set V to be processed is extractedm×n, the row m of data set represents sample, and column n represents feature；
2) by data set Vm×nNon-negativeization, normalized are carried out,
In formula: i=1,2 ..., m；J=1,2 ..., n, maxVijFor column vector VjMaximum value；minVkjFor column vector VjMinimum value；
3) multiple two classification problems will be divided into according to permutation and combination method the problem of original multistream heat exchanger, it is assumed that Vm×nContaining N class sample, then the corresponding characteristic set of two classification problem of each divided is expressed as Pi, wherein
4) to each non-negative characteristic setIt is decomposed using least-squares iteration algorithm, i.e. Pi= WiHi；
Random initializtion WiAnd Hi, low-dimensional Embedded dimensions riPreferential selection is identical as sample class number, and Non-negative Matrix Factorization obtains To basic matrix WiWith coefficient matrix Hi, rule of iteration is as follows:
In formula:Wi is characterized set PiThe basic matrix that Non-negative Matrix Factorization obtains,Indicate group moment Battle array WiTransposition, HiIt is characterized set PiThe coefficient matrix that Non-negative Matrix Factorization obtains,Indicate coefficient matrix HiTransposition；
5) to basic matrix WiWith coefficient matrix HiCarry out thermal map Visualization, basic matrix WiRow correspond to sample, coefficient Matrix HiColumn correspond to primitive character；
6) basic matrix W is observediFeature clustering situation, if in basic matrix WiWherein a column are it is observed that two class samples are obvious It separates, then carries out step 7), otherwise reselect low-dimensional Embedded dimensions ri, return step 4)；
7) characteristic of division F is selected using significant expression principle in thermal mapi, special by adjusting thermal map threshold value control tactics Levying number is 1；
8) the characteristic of division F that all two classification problems are acquirediUnion operation is done, final characteristic of division set F is obtained,
The invention has the benefit that the method for the present invention can be realized cooperating and having complementary advantages for computer and people, The result interpretation of selection is strong, ensure that the good of low-dimensional character subset while carrying out dimensionality reduction to original higher-dimension primitive character Good classification performance.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart.
Fig. 2 is data set P in embodiment1The Non-negative Matrix Factorization result thermal map of (the one or two class sample set) visualizes effect Fruit figure.
Fig. 3 is data set P in embodiment2The Non-negative Matrix Factorization result thermal map of (the first three classes sample set) visualizes effect Fruit figure.
Fig. 4 is data set P in embodiment3The Non-negative Matrix Factorization result thermal map of (the second three classes sample set) visualizes effect Fruit figure.
Fig. 5 is wine data set features 1,7 and 12 three-dimensional visualization effect pictures in embodiment.
Specific embodiment
It elaborates with reference to the accompanying drawings and examples to the present invention, the implementation case is for Wine in UCI data set Data set expansion, Wine data set derive from the chemical analysis results of three kinds of different cultivars grape wine, which has determined three kinds The concrete content of 13 kinds of ingredients in grape wine, Wine data set contain three classes data and amount to 178 samples, 13 kinds of characteristic attributes (ingredient), the sample number of every one kind are respectively as follows: 59 (classes one), 71 (classes two), 48 (classes three), the present embodiment to this 13 kinds of features into Row feature selecting selects the good feature of classification performance.
Referring to Fig.1, a kind of visualization feature selection method based on the classification Non-negative Matrix Factorization of failure two, including following step It is rapid:
1) data set V to be processed is extractedm×n, the row m of data set represents sample, and column n represents feature, the present embodiment Using Wine data set；
2) by data set Vm×nNon-negativeization, normalized are carried out,
In formula: i=1,2 ..., m；J=1,2 ..., n, maxVijFor column vector VjMaximum value；minVkjFor column vector VjMinimum value；
3) multiple two classification problems will be divided into according to permutation and combination method the problem of original multistream heat exchanger, it is assumed that Vm×nContaining N class sample, then the corresponding characteristic set of two classification problem of each divided is expressed as Pi, whereinWine data set is divided into 3 two classification problems, respectively P according to permutation and combination principle by the present embodiment1 (the one or two class sample set), P2(the first three classes sample set), P3(the second three classes sample set)；
4) to each non-negative characteristic setIt is decomposed using least-squares iteration algorithm, i.e. Pi= WiHi；
Random initializtion WiAnd Hi, low-dimensional Embedded dimensions riPreferential selection is identical as sample class number, and Non-negative Matrix Factorization obtains To basic matrix WiWith coefficient matrix Hi, rule of iteration is as follows:
In formula:WiIt is characterized set PiThe basic matrix that Non-negative Matrix Factorization obtains,Indicate basic matrix WiTransposition, HiIt is characterized set PiThe coefficient matrix that Non-negative Matrix Factorization obtains,Indicate coefficient matrix HiTransposition；
5) to basic matrix WiWith coefficient matrix HiCarry out thermal map Visualization, basic matrix WiRow correspond to sample, coefficient Matrix HiColumn correspond to primitive character；
6) basic matrix W is observediFeature clustering situation, if in basic matrix WiWherein a column are it is observed that two class samples are obvious It separates, as shown in Fig. 2, then carrying out step 7), otherwise reselects low-dimensional Embedded dimensions ri, return step 4)；
In terms of cluster angle, two category features should be substantially contained only in the characteristic set of two classification problems, can be distinguished With the feature that cannot distinguish between two classification problems, other features can be combined to obtain by these two types of substantive characteristics；Thus, the present embodiment To P1、P2、P3When carrying out Non-negative Matrix Factorization, low-dimensional Embedded dimensions r preferentially selects 2, the Visualization of final decomposition result As shown in Figure 2,3, 4；
7) using significant expression principle in thermal map, i.e., according to matrix multiple rule, what big number × big number obtained still can It is big number, comes with value distinguishing small in thermal map；Pass through coefficient matrix HiPrimitive character corresponding to big number regions is selected point Category feature Fi, by adjusting control of the thermal map threshold value realization to characteristic of division number, usual controlling feature number is 1；
8) the characteristic of division F that all two classification problems are acquirediUnion operation is done, final characteristic of division set F is obtained,
The present embodiment is using the significant expression principle of thermal map successively to P1、P2、P3Decomposition result carry out characteristic of division choosing It selects；By adjusting the display threshold of thermal map, controlling the characteristic of division number that each two classification problem is selected is 1, then most The characteristic of division selected eventually it is found that be successively characterized 1, feature 7 and feature 12, is obtained by coefficient matrix H after union is taken to it Characteristic of division collection is combined into { 1,7,12 }.
The three-dimensional that the 1st dimension, the 12nd dimensional feature of the 7th peacekeeping in the present embodiment extraction wine data set draw the data set can Depending on changing effect picture, as shown in figure 5, it may be seen that can be good using the grape wine of three kinds of different cultivars of the method for the present invention It distinguishes, under KNN classifier, the classification rate of subset F has reached 94.94%.
Illustrated by use above, the method for the present invention can make feature selecting become visual pattern, and the result of selection can It is explanatory strong, it ensure that the nicety of grading of selected character subset, can contribute to solution complex electromechanical systems monitoring and examined with failure Disconnected High dimensional data analysis improves the efficiency and accuracy of fault diagnosis.

Claims (1)

1. a kind of visualization feature selection method based on the classification Non-negative Matrix Factorization of failure two, which is characterized in that including following Step:
1) data set V to be processed is extractedm×n, the row m of data set represents sample, and column n represents feature；
2) by data set Vm×nNon-negativeization, normalized are carried out,
In formula: i=1,2 ..., m；J=1,2 ..., n, maxVijFor column vector VjMaximum value；minVkjFor column vector Vj's Minimum value；
3) multiple two classification problems will be divided into according to permutation and combination method the problem of original multistream heat exchanger, it is assumed that Vm×nContain There is N class sample, then the corresponding characteristic set of two classification problem of each divided is expressed as Pi, wherein
4) to each non-negative characteristic setIt is decomposed using least-squares iteration algorithm, i.e. Pi=WiHi；
Random initializtion WiAnd Hi, low-dimensional Embedded dimensions riPreferential selection is identical as sample class number, and Non-negative Matrix Factorization obtains base Matrix WiWith coefficient matrix Hi, rule of iteration is as follows:
In formula:WiIt is characterized set PiThe basic matrix that Non-negative Matrix Factorization obtains,Indicate basic matrix Wi's Transposition, HiIt is characterized set PiThe coefficient matrix that Non-negative Matrix Factorization obtains,Indicate coefficient matrix HiTransposition；
5) to basic matrix WiWith coefficient matrix HiCarry out thermal map Visualization, basic matrix WiRow correspond to sample, coefficient matrix HiColumn correspond to primitive character；
6) basic matrix W is observediFeature clustering situation, if in basic matrix WiWherein a column are it is observed that two class samples are clearly separated, Step 7) is then carried out, low-dimensional Embedded dimensions r is otherwise reselectedi, return step 4)；
7) characteristic of division F is selected using significant expression principle in thermal mapi, by adjusting thermal map threshold value control tactics feature Number is 1；
8) the characteristic of division F that all two classification problems are acquirediUnion operation is done, final characteristic of division set F is obtained,
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