CN106529594B - Supervision dimension reduction method applied to big data Activity recognition - Google Patents

Abstract

The present invention relates to a kind of supervision dimension reduction methods applied to big data Activity recognition, association linear approximation rarefaction representation LASRC fast classification algorithm can retain the classification information of data when the behavioral data of higher-dimension is projected to a lower dimensional space, realize effective reduction of data dimension, OP-LASRC is standard with classification residual error, pursue a linear orthogonal projection, this give the supervisory roles of OP-LASRC, the small feature with disagreement information is converted by the behavior picture of higher-dimension to classify, number of computations is few, storage can be reduced and improve classification effectiveness, to which LASRC fast classification algorithm reaches higher identification.OP-LASRC algorithm is verified from accuracy, speed, robustness on KTH behavior database, to verify OP-LASRC energy perfect matching LASRC algorithm, it is associated with the structure of dimensionality reduction and classification, the system that can form an Activity recognition efficiently applies to the Activity recognition of big data.

Description

Supervision dimension reduction method applied to big data Activity recognition

Technical field

The present invention relates to a kind of image data processing technique, in particular to a kind of supervision applied to big data Activity recognition Dimension reduction method.

Background technique

Human bodys' response is the research hotspot in pattern-recognition and field of machine vision by extensive concern, not only in intelligence Monitoring, motion analysis, identity identifies and human-computer interaction aspect has vast application prospect, and in the different of security risk place Normal behavior monitoring, as traffic accident, Electrical Safety, medical monitoring etc. have great importance (document 1Chen L, Wei H, J Ferryman.Asurvey of human motion analysis using depth imagery [J] .Pattern Recognition Letters, 2013,34 (15): 1995-2006).The behavior act of human body target spatially shows multiple Polygamy, it is just single dynamic when describing spatiotemporal motion variation of the target in two-dimensional image sequence in the Human bodys' response of big data Multiframe picture need to be just acquired for work in monitor video, the training data of the human body behavior composition of a variety of quantity is often huge , a large amount of calculating time is needed when to these data processings.But all in all two-dimensional Activity recognition speed than it is three-dimensional more Fastly (document 2 Gu Junxia, Ding Xiaoqing, Wang Shengjin automate journal based on 2D Activity recognition [J] of human body behavior 3D model, 2010,36 (1): 46-53), suitable for the Activity recognition of big data, how in the case where illumination, visual angle and background difference, Classification quick to the behavior of two-dimensional big data, accurate, stable is still the problem (document for being badly in need of research in Activity recognition 3Candamo J, Shreve M, Goldgof D B, et al.Under-standing Transit Scenes:A Survey on Human Behavior-Recognition Algorithms[J].IEEE Transactions on Intelligent Transportation Systems, 2010,11 (1): 206-224).In order to reach this target, domestic and foreign scholars are from dimensionality reduction (document 4 Huang Kaiqi, Chen Xiaotang, Kang Yun, wait intelligent Video Surveillance Technology comprehensive with numerous studies have been done in terms of acceleration classifier two State [J] Chinese journal of computers, 2015 (6): 1093-1118).

In past 20 years, various classifiers are proposed by domestic and foreign scholars, but are ground to the Activity recognition classifier of big data Study carefully very few, this classifier will not only be suitble to the data type of multi-quantity behavior, also to guarantee Activity recognition quickly, it is accurate, steady It is fixed.Traditional classifier has support vector machines (SVM) and k- neighbour (NN), and (Ren Xiaofang, Qin Jianyong, Yang Jie wait to be based on to document 5 Application [J] the computer application of the LS-TSVM of energy model in human action identification is studied, 2016,33 (2): 598-601) With the LS-TSVM classification method based on energy model, using two hyperplane, each hyperplane introduces energy parameter and makes an uproar to reduce The influence of sound and exceptional value, improves recognition efficiency.But the SVM classifier deficiency big there is also optimization difficulty, calculating intensity.Text Offer 6 (Liu L, Shao L, Rockett P.Human action recognition based on boosted feature selection and naive Bayes nearest-neighbor classification[J].Signal Processing, 2013,93 (6): 1521-1530) NB-NN algorithm classification is used, which does not need the training time, only needs to inquire The sample of the smallest distance is obtained, but its discrimination need to be improved.John Wright proposition SRC (document 7Wright J, Yang A Y, Ganesh A, et al.Robust Face Recognition via Sparse Representation [J] .IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009,31 (2): 210-227) algorithm, the algorithm to block, noise, illumination have extremely strong robustness and it is famous.Document 8 (Liu C, Yang Y, Chen Y.Human Action Recognition using Sparse Representation[C].IEEE International Conference on Intelligent Computing and Intelligent Systems, 2009,4:184-188) SRC is used for Activity recognition, recognition correct rate ratio NN algorithm is higher, but consumes in the solution of L1 norm The a large amount of time, in order to accelerate classification speed, (Zhang L, Yang M, the Feng X.Sparse representation of document 9 Or collaborative representation:Which helps face recognition? [C] .International Conference on Computer Vision, 2011,6669 (5): 471-478) propose collaboration table Show classification (CRC) algorithm, is solved using L2 norm, substantially increase recognition efficiency, but reduce the robustness of algorithm.Document 10 (Ortiz E G, Becker B C.Face recognition for web-scale datasets [J] .Computer Vision and Image Understanding, 2014,118 (1): 153-170) propose LASRC algorithm first use L2 model Number quickly estimates coefficient vector, screens to sample database, and the corresponding sample of k greatest coefficient before finding forms low capacity Sample after classified with SRC, the speed of algorithm is accelerated, so being able to achieve the picture to big quantity using LASRC sorting algorithm Fast Classification, research find to be used in the Activity recognition of big data.

Computationally intensive since LASRC classifier is classified for big data, there is still a need for improve for speed.The behavior of higher-dimension Data can include a large amount of irrelevant information and redundancy (11 Hu Jie of document, high dimensional data Feature Dimension Reduction Review Study [J], meter Calculation machine application study, 2008,25 (09): 2601-2606) dimension disaster can be caused, this will seriously affect speed when data classification Degree, is to select low-dimensional characteristic set from an initial high dimensional feature set using Feature Dimension Reduction, can substantially increase classification effect Rate.Classical dimension reduction method has principal component analysis (PCA) (document 12Turk M A, Pentland AP.Face recognition using eigenfaces[C].in Proceedings of the 1991IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), 1991:586- And linear discriminant analysis (LDA) (document 13Belhumeur P, Hespanha P, Kriegman D.recognition 591) Using class specific linear projection [J] .IEEE TransPatternAnal Mach Intell, 1997,19 (7): 711-720) algorithm, PCA, which is non-supervisory dimensionality reduction, finds mapping matrix by maximizing variance, and LDA is then supervision Dimensionality reduction disperses to obtain projection matrix by dispersing between maximization class and minimizing this class, and both methods is not disclosed and is embedded in The critical data of high dimensional nonlinear data space.In order to overcome this limitation, the dimension reduction method of a kind of popular study is suggested, passes through Allusion quotation is locality preserving projections (LPP) (document 14He X, Yan S, Hu Y, et al.Face recognition using laplacianfaces[J].IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005,27 (3): 328-40) algorithm, it is assumed that low-dimensional data samples a potential stream in higher dimensional space In shape, this algorithm not being subjected to supervision does not account for class label, there are also Shortcomings when classification, document 15 (Zhao Z S, Zhang L, Zhao M, et al.Gabor face recognition by multi-channel classifier Fusion of supervised kernel manifold learning [J] Neurocomputing, 2012,97:398- 404) propose that popular study dimensionality reduction (SLPP) based on supervision core enhances this class by similar matrix using class label information Information, information carrys out dimensionality reduction between weakening class, this allows classification to reach better effect.

Although supervision dimensionality reduction is conducive to preferably classify, above-mentioned dimension reduction method and rarefaction representation classification method be not direct Association, (Qiao L S, Chen S C, the Tan X Y.Sparsity preserving projections with of document 16 Applications to face recognition [J] .Pattern Recognition, 2010,43:331-341) it proposes Sparse retaining projection (SPP) using all one given samples of training sample rarefaction representation and seeks a linear projection, So that rarefaction representation coefficient is saved.(Yang J, Chu D, Zhang L, the et al.Sparse of document 17 representation classifier steered discriminative projection with applications To face recognition [J] .IEEE Transaction son Neural Networks&Learning Systems, 2013,24 (7): 1023-1035) propose that the nature of dimensionality reduction and classification is established in rarefaction representation classification control disagreement projection (SRC-DP) Connection, using the residual computations rule of SRC algorithm, the judgment criteria new as one carrys out controlling feature extraction, which obtains Projection matrix needs to iterate to calculate, and consumes duration, is unfavorable for the Activity recognition of big data.Document 18 (Hua J, Wang H, Ren M, et al.Dimension Reduction Using Collaborative Representation Reconstruction Based Projections [J] .Neurocomputing, 2016,193:1-6) and 19 (Yin of document J, Wei L, Song M, et al.Optimized projection for Collaborative Representation based Classification and its applications to face recognition[J].Pattern Recognition Letter, 2016,73:83-90) the method is used in CRC algorithm, collaboration presentation class control disagreement is thrown Shadow (CRC-DP) algorithm dimensionality reduction can be improved efficiency in classification, but dimensionality reduction is former needs to iterate to calculate.In order to solve iteration duration Consumption problem, (Lu C Y, the Huang D S.Optimized projections for sparse of document 20 Representation based classification [J] .Neurocomputing, 2013,113:213-219) it proposes Optimization projection directly calculates projection matrix for supervising dimensionality reduction to rarefaction representation classification (OP-SRC) algorithm, and matches SRC points Class improves the classification effectiveness of SRC.

Summary of the invention

The present invention be directed to the low problems of real-time difference when the Human bodys' response of big data and discrimination, propose one kind Applied to the supervision dimension reduction method of big data Activity recognition, the thought based on OP-SRC proposes that optimization projection is dilute to linear approximation The supervision dimension reduction method of presentation class OP-LASRC is dredged, is associated with linear approximation rarefaction representation LASRC rapid classification method for higher-dimension Behavioral data can retain the classification informations of data when projecting to a lower dimensional space, realize effective reduction of data dimension, OP-LASRC is standard with classification residual error, pursues a linear orthogonal projection, this give the supervisory roles of OP-LASRC, will be high The behavior picture of dimension is converted into the small feature with disagreement information to classify, and number of computations is few, can reduce storage and improve classification Efficiency, so that LASRC rapid classification method reaches higher identification.From accuracy, speed, robust on KTH behavior database Property verify OP-LASRC method, thus verify OP-LASRC can perfect matching LASRC method, be associated with the knot of dimensionality reduction and classification Structure, the system that can form an Activity recognition efficiently apply to the Activity recognition of big data.

The technical solution of the present invention is as follows: a kind of supervision dimension reduction method applied to big data Activity recognition, specifically include as Lower step:

1), to training sample principal component analysis PCA dimension-reduction treatment, keeping characteristics information；

2) complete dictionary A, was made of the training sample after dimensionality reduction,

A=[A₁,A₂,.....,A_c]=[v_1,1,v_1,2,....v_1,j,v_2,1,v_2,2......v_i,j], i=c, j=e,

A=[A₁,A₂,.....,A_c]∈R^N×M, A is the matrix of N row M column, shares c class, every class has e width figure, altogether c × e=n width figure, each sample are v_{I, j},

Each training sample is isolated in order regards test sample y,

For the training sample linear expression of each test sample y:

Y=α_i,1v_i,1+α_i,2v_i,2+α_i,3v_i,3+...+α_i,jv_i,j=Ax₀

Wherein x₀It is equation coefficient vector, if x₀It is sparse, a kind of training ideally related with test sample Coefficient non-zero before sample, other coefficients are all 0, when n is sufficiently large, x₀It indicates are as follows:

x₀=[0 ..., 0, α_i,1,α_i,2,...,α_i,j,0,...,0]^T

Coefficient vector x₀, can be by solving equation y=Ax₀It obtains, can first become the Solve problems of L2 norm:

Use formulaCalculate corresponding sparse coefficient

3), this class reconstructed residual R is calculated with following formula_WThe reconstructed residual R between class_B, and with formula (β R_B-R_W)p_k=λ_kp_k, k=1,2 ..., d,Seek matrix P；P=[p₁,p₂,....p_k,]；λ_kIt is β R_B-R_WCharacteristic value, p_kIt is pair The feature vector answered makes reconstructed residual between class big as far as possible, selects maximum standard to make this class reconstructed residual small as far as possibleMatrix P is corresponding by d maximum characteristic values Feature vector composition, β is a constant parameter, for balancing the information of reconstructed residual between this class reconstructed residual and class,

δ_l(x₀) it is entire sparse coefficient,For the sparse coefficient of every one kind；

4), be subjected to supervision matrix B=P after dimensionality reduction^TA, B replace the solution for first becoming L2 norm in A matrix step 2) to ask Topic, then use formulaEstimate corresponding sparse coefficient

5), from sparse coefficientIn select before w maximum coefficients, find the classification of corresponding training sample, these The new complete dictionary Ω of the training sample composition of class, test sample are expressed as y=Ω x₀；

6), for y=Ω x obtained by step 5)₀, it is solved by L1 norm, solution formula:λ is sparse control coefrficient, and solution obtains sparse coefficient x₀；

7), pass through formulaCalculate residual error r_i(y), the smallest one kind of residual error, as knows Other result.

The beneficial effects of the present invention are: the present invention is applied to the supervision dimension reduction method of big data Activity recognition, from dimensionality reduction Start with in terms of Fast Classification two, the OP-LASRC method matching LASRC of proposition is used successfully to big data Activity recognition.Wherein The Fast Classification of LASRC is that sparse coefficient is quickly calculated by L2 norm, and k maximum coefficients form new training sample before selecting This, successfully excludes the very big sample of difference, and is accurately calculated to the sample database after diminution with L1 norm, it is ensured that identification Rate, the reduction of sample size can reduce the width of training sample data.Dimensionality reduction is to supervise dimensionality reduction with OP-LASRC, by higher-dimension Image data optimization retains disagreement feature when projecting to low-dimensional data, and this low-dimensional data with disagreement feature can allow sparse The residual computations of presentation class avoid Errors Catastrophic, and from high discrimination is realized, lack the effect that data volume is calculated, and keep The characteristics of strong robustness that rarefaction representation classification is calculated, dimensionality reduction then reduces the height of training sample data.From the point of view of experiment, identification Rate 96.5%, strong robustness, the execution time is shorter, illustrates that OP-LASRC can allow classification to reach height with LASRC perfect matching Effect.This mode that data processing amount is reduced in terms of width and height two, opens one for the Activity recognition of big data New thinking.

Detailed description of the invention

Fig. 1 is under 4 samples of the invention using PCA, LDA, LPP dimensionality reduction and OP-LASRC dimension reduction method totality discrimination and dimension The relationship comparison diagram of degree；

Fig. 2 is under 5 samples of the invention using PCA, LDA, LPP dimensionality reduction and OP-LASRC dimension reduction method totality discrimination and dimension The relationship comparison diagram of degree；

Fig. 3 is under 6 samples of the invention using PCA, LDA, LPP dimensionality reduction and OP-LASRC dimension reduction method totality discrimination and dimension The relationship comparison diagram of degree；

Fig. 4 is under 7 samples of the invention using PCA, LDA, LPP dimensionality reduction and OP-LASRC dimension reduction method totality discrimination and dimension The relationship comparison diagram of degree；

Fig. 5 is that test sample of the present invention adds noise damage figure.

Specific embodiment

One, principle: OP-LASRC method

OP-LASRC method is a kind of method of the optimization projection telltale in PCA dimensionality reduction.By a higher-dimension When data projection is to a low-dimensional data, retains disagreement feature, be just to maintain the category label of picture, this disagreement information is to dilute It is particularly important to dredge presentation class.

In LASRC classification method, need to constitute complete dictionary A=[A₁,A₂,.....,A_c]∈R^N×M, (A is a N The matrix of row M column) c class is shared, every class has e width figure, altogether c × e=n width figure, wherein every one kind image A_iIt indicates, i=1, 2 ... c, each sample are v, A_i=[v_i,1,v_i,2,v_i,3,.......v_i,j], j=e, excessively complete dictionary A may be expressed as:

A=[A₁,A₂,.....,A_c]=[v_1,1,v_1,2,....v_1,j,v_2,1,v_2,2......v_i,j]

Training sample linear expression can be used for each test sample y:

Y=α_i,1v_i,1+α_i,2v_i,2+α_i,3v_i,3+...+α_i,jv_i,j=Ax₀

Wherein x₀It is equation coefficient vector, if x₀It is sparse, a kind of training ideally related with test sample Coefficient non-zero before sample, other coefficients are all 0, when n is sufficiently large, x₀It indicates are as follows:

x₀=[0 ..., 0, α_i,1,α_i,2,...,α_i,j,0,...,0]^T

Coefficient vector x₀, can be by solving equation y=Ax₀It obtains, can first become the Solve problems of L2 norm:

Above formula can calculate sparse coefficient by pseudo inverse matrix

Pseudo inverse matrix calculating ratio L1 norm solves more convenient, the speed with least square method.FromIn select Preceding w maximum coefficients find out the corresponding training sample of this w greatest coefficient and form a new excessively complete dictionary Ω, test Sample is represented by y=Ω x₀.This equation is solved using L1 norm:

λ is sparse control coefrficient, takes 0.01 according to λ in document 10.

With the sparse coefficient of every one kindCalculate residual error:

Recognition result:

I (y)=minr_i(y) (5)

It is easy discovery, LASRC method can be used in the Activity recognition of big data.But it for excessively complete dictionary A, can use One mapping matrix P ∈ R^d, (P is a matrix for d column, d < < N), in y=P^TUnder v linear transformation, sample v can be reflected from N-dimensional It is mapped to d dimension, each sample v_{I, j}Y can be passed through_i,j=P^Tv_i,jConversion is calculated, a new dictionary B=is obtained after conversion P^TA.This new dictionary just replaces original complete dictionary A, is brought into LASRC method and calculates least residual, is identified As a result.

Isolate a sample y in order from training sample_{I, j}As test sample, pass through the pseudo inverse matrix of above formula (2) Calculate coefficient vector x₀, use δ_l(x₀) indicate entire sparse coefficient, it usesIndicate the sparse coefficient of every one kind, and residual error

Define this class reconstructed residual is defined as:

Reconstructed residual between definition class is defined as:

Count residual matrix is defined as:

In order to obtain better recognition result by the minimum value of residual error in the implementation procedure of LASRC method, it should It makes this class reconstructed residual small as far as possible, makes reconstructed residual between class big as far as possible, select maximum standard:

β is a constant parameter, can balance the information of reconstructed residual between this class reconstructed residual and class, according to reference text It offers 10, β and takes 0.25.B=P^TA, then being easy to getWithSo:

J (P)=tr (P^T(βR_B-R_W)P) (11)

Falling in order to prevent needs P=[p₁,p₂,....p_k,] it is that unit vector is constituted, and is worked asCertainly there are also other constrained procedures, such as: can enable tr (P^TR_WP it)=1 then maximizes tr(P^TR_BP).It is required thatIt can produce a rectangular projection, retain the distributed architecture of data, therefore objective function can To be reconstructed into optimization problem:

Above-mentioned objective function is converted with Lagrange multiplier are as follows:

Above formula is to P_kDerivation derivation simultaneously enables it be equal to 0:

It is available:

(βR_B-R_W)p_k=λ_kp_k, k=1,2 ..., d (15)

λ_kIt is β R_B-R_WCharacteristic value, P_kIt is corresponding feature vector, then:

P is formed by by the corresponding feature vector of the maximum characteristic value of d, it can be found that J (P) is maximized.It is orthogonal P and the β R of change_B-R_WIt is symmetrical, then being multiplied by matrix P when dimensionality reduction just forms a kind of method for supervising rectangular projection, this projection A large amount of disagreement information can be remained, is classified to LASRC highly beneficial.Obtained P matrix is a kind of effect for supervising dimensionality reduction, that Before method execution, PCA Principal Component Analysis dimensionality reduction is first used, sample formed complete dictionary A after dimensionality reduction, can obtain B= P^TA, obtained dictionary B be still it is complete, be used further to LASRC classification, it will improve recognition efficiency.

Two, method flow:

Step 1: to training sample and test specimens sample y PCA dimension-reduction treatment, keeping characteristics information.

Step 2: being made of complete dictionary A the training sample after dimensionality reduction, isolates each training sample in order and regards Test sample calculates corresponding sparse coefficient with formula (2).

Step 3: reconstructed residual between this class reconstructed residual and class is calculated with formula (10), and obtains matrix with formula (15) P。

Step 4: matrix B=P after the dimensionality reduction that is subjected to supervision^TA is standardized with L2, then B replaces A matrix to be estimated with formula (2) Corresponding sparse coefficient

Step 5: from sparse coefficientIn select before k maximum coefficients, find the classification of corresponding training sample, The new complete dictionary Ω of the training sample composition of these classes.

Step 6: it is solved to obtain sparse coefficient x with L1 norm by formula (3)₀。

Step 7: residual error, the smallest one kind of residual error, as recognition result are calculated by formula (4).

Three, it tests

1, accuracy is tested

The method is verified, selects KTH behavior database as experimental data.In test using PCA, LDA, LPP dimensionality reduction and The comparison of OP-LASRC dimensionality reduction, then classified with LASRC.Drop to different dimensions, discrimination is different, overall discrimination and dimension Relationship is as shown in Figures 1 to 4.The number of every one kind sample also will affect discrimination, which can be used 4,5,6,7 sample numbers, The every class in original sample library acquires 10 figures, if 5 width therein regards training sample, in addition 5 width figures regard test sample, Successively test takes average discrimination.Fig. 1 to 4 is respectively that 4 samples, 5 samples, 6 samples and 7 samples use PCA, LDA, LPP dimensionality reduction With the relationship comparison diagram of OP-LASRC dimensionality reduction totality discrimination and dimension.

As it can be seen that different sample numbers, discrimination is different, and with the increase of dimension, discrimination is also increased, and is arrived in Fig. 1 to 4 When 200 dimension, discrimination basically reaches peak.Can clearly be seen in figure OP-LASRC dimensionality reduction discrimination ratio PCA, LDA, The discrimination of LPP dimensionality reduction is high, and the maximum average recognition rate of OP-LASRC difference sample number is: 4 samples 93%, 5 samples 96.5%, 6 samples 96.8%, 7 samples 97.0%.Discrimination after OP-LASRC dimensionality reduction on discrimination than PCA, LDA, LPP Height illustrates the feasibility of OP-LASRC, this is the accurate premise of Activity recognition.

2, comparison of classification is tested

It when LASRC method is subjected to supervision dimensionality reduction to 200 dimension, is compared, has with the maximum average recognition rate of other algorithms Body result six kinds of algorithm discriminations of visible the following table 1:

For other algorithms, the LASRC method discrimination ratio NB-NN (document 6) for the dimensionality reduction that is only subjected to supervision, Linear SVM (Moayedi F, Azimifar Z, Boostani R.Structured sparse representation for Human action recognition [J] .Neurocomputing, 2015,161 (C): 38-46), CRC (document 9) algorithm Discrimination is high, has same discrimination with SRC (document 7) algorithm, and without the LASRC method for the dimensionality reduction that is subjected to supervision, discrimination is only Have 85.4%, it can be seen that after OP-LASRC supervises dimensionality reduction, can guarantee that LASRC occupies some superiority on discrimination.

Table 1

3, robustness is tested:

LASRC method improves recognition speed on the basis of SRC algorithm, does not influence its accuracy and robustness still, Noise is added to test sample in the test, 1~5 width figure damaged in percentage such as Fig. 5, Fig. 5 of picture is separately added into: mean value is 0, variance corresponds to 0.2,0.5,0.1,0.2,0.3 Gaussian noise.Dimensionality reduction is supervised using PCA dimensionality reduction and OP-LASRC when classification To 200 dimensions, tested with 5 sample classifications, discrimination such as table 2.

According to table 2 as can be seen that when picture is destroyed than lower than 60%, the discrimination of OP-LASRC supervision dimensionality reduction remains to protect It holds 90% or more, totality is higher than the discrimination of PCA dimensionality reduction, illustrates in the case where OP-LASRC supervises dimensionality reduction, although data are reduced, The robustness of LASRC method is still very strong.

Table 2

。

Claims (1)

1. a kind of supervision dimension reduction method applied to big data Activity recognition, which is characterized in that specifically comprise the following steps:

1), to training sample principal component analysis PCA dimension-reduction treatment, keeping characteristics information；

2) complete dictionary A, was made of the training sample after dimensionality reduction,

A=[A₁,A₂,.....,A_c]=[v_1,1,v_1,2,....v_1,j,v_2,1,v_2,2......v_i,j], i=c, j=e,

A=[A₁,A₂,.....,A_c]∈R^N×M, A is the matrix of N row M column, shares c class, every class has e width figure, altogether c × e =n width figure, each sample are v_{I, j},

Each training sample is isolated in order regards test sample y,

For the training sample linear expression of each test sample y:

Y=α_i,1v_i,1+α_i,2v_i,2+α_i,3v_i,3+...+α_i,jv_i,j=Ax₀

Wherein x₀It is equation coefficient vector, if x₀It is sparse, a kind of training sample ideally related with test sample The coefficient non-zero of front, other coefficients are all 0, when n is sufficiently large, x₀It indicates are as follows:

x₀=[0 ..., 0, α_i,1,α_i,2,...,α_i,j,0,...,0]^T

Coefficient vector x₀, can be by solving equation y=Ax₀It obtains, can first become the Solve problems of L2 norm:

Use formulaCalculate corresponding sparse coefficient

3), this class reconstructed residual R is calculated with following formula_WThe reconstructed residual R between class_B, and with formula (β R_B-R_W)p_k=λ_kp_k, k= 1,2 ..., d,Seek matrix P；P=[p₁,p₂,....p_k,]；λ_kIt is β R_B-R_WCharacteristic value, p_kIt is corresponding spy Vector is levied,

To make this class reconstructed residual small as far as possible, makes reconstructed residual between class big as far as possible, select maximum standardMatrix P is corresponding by d maximum characteristic values Feature vector composition, β is a constant parameter, for balancing the information of reconstructed residual between this class reconstructed residual and class,

δ_l(x₀) it is entire sparse coefficient,For the sparse coefficient of every one kind；

4), be subjected to supervision matrix B=P after dimensionality reduction^TA, B replace the Solve problems for first becoming L2 norm in A matrix step 2), then Use formulaEstimate corresponding sparse coefficient

5), from sparse coefficientIn select before w maximum coefficients, find the classification of corresponding training sample, the instruction of these classes Practice the new complete dictionary Ω of sample composition, test sample is expressed as y=Ω x₀；

6), for y=Ω x obtained by step 5)₀, it is solved by L1 norm, solution formula:λ is sparse control coefrficient, and solution obtains sparse coefficient x₀；

7), pass through formulaCalculate residual error r_i(y), the smallest one kind of residual error, as identification knot Fruit.