Weighted Sparse Image Classification Based on Low Rank Representation

Transcription

1 Copyrght 08 Tech Scence Press CMC, vol.56, no., pp.9-05, 08 Weghted Sparse Image Classfcaton Based on Low Rank Representaton Qd Wu, Ybng L, Yun Ln, * and Ruoln Zhou Abstract: The conventonal sparse representaton-based mage classfcaton usually codes the samples ndependently, whch wll gnore the correlaton nformaton exsted n the data. Hence, f we can explore the correlaton nformaton hdden n the data, the classfcaton result wll be mproved sgnfcantly. To ths end, n ths paper, a novel weghted supervsed spare codng method s proposed to address the mage classfcaton problem. The proposed method frstly explores the structural nformaton suffcently hdden n the data based on the low rank representaton. And then, t ntroduced the extracted structural nformaton to a novel weghted sparse representaton model to code the samples n a supervsed way. Expermental results show that the proposed method s superorty to many conventonal mage classfcaton methods. Keywords: Image classfcaton, sparse representaton, low-rank representaton, numercal optmzaton. Introducton Image classfcaton s a fundamental ssue n computer vson, whch ams to classfy an mage nto an accurate category. Many lteratures about mage classfcaton are emerged n the past two decades [Lu, Fu and He (07)], and several classfcaton frameworks are formed to address the classfcaton problem of vson task. Durng the mentoned frameworks, sparse-based classfcaton attracted many attentons and are wdely studed n recent years. Sparse sgnal representaton has proven to be an extremely powerful tool for acqurng, representng, and compressng hgh-dmensonal sgnals [Wrght, Ma, Maral et al. (00)]. In the past few years, sparse representaton has been appled to many vson tasks, ncludng face recognton [Yang, Zhang, Yang et al. (0); Lu, Tran and Sang (06)], mage super-resoluton [Yang, Chu and Wang (00); Yang, Wrght, Huang et al. (00)], denosng and npantng [Fadl, Starck and Murtagh (03); Guleryuz (006)], and mage classfcaton [Kulkarn and L (0); Thagarajan and Spanas (0)]. Due to ts wde applcablty, people conducted detaled research on mage classfcaton based on sparse representaton and acheved remarkable results [Tang, Huang and Xue (06); Gao, Tsang and Cha (00); Lu, Fu and He (07)]. College of Informaton and Communcaton Engneerng, Harbn Engneerng Unversty, Harbn, 5000, Chna. Department of Electrcal and Computer Engneerng, Western New England Unversty,USA. * Correspondng Author: Yun Ln. Emal: lnyun@hrbeu.edu.cn. CMC. do:0.3970/cmc

2 9 Copyrght 08 Tech Scence Press CMC, vol.56, no., pp.9-05, 08 Accordng to the pcture type, mage classfcaton s manly appled n certan specfc felds such as face recognton and hyperspectral mage classfcaton and remote sensng mage classfcaton. In face recognton, based on a sparse representaton computed by l -mnmzaton, Wrght et al. [Wrght, Ma, Maral et al. (00)] proposed a general classfcaton algorthm for (mage-based) object recognton [Wrght, Ganesh, Zhou et al. (009)]. Ths new framework provded new nsghts nto two crucal ssues n face recognton: feature extracton and robustness to occluson. The theory of sparse representaton helped predct how much occluson the recognton algorthm could handle and how to choose the tranng mages to maxmze robustness to occluson. Recent research has shown the speed advantage of extreme learnng machne (ELM) and the accuracy advantage of sparse representaton classfcaton (SRC) n the area of mage classfcaton. In order to unfy such mutual complementarty and thus further enhance the classfcaton performance, Cao et al. [Cao, Zhang, Luo et al. (06)] proposed an effcent hybrd classfer to explot the advantages of ELM and SRC n Cao et al. [Cao, Zhang, Luo et al. (06)]. Whle the mportance of sparsty s much emphaszed n SRC and many related works, the use of collaboratve representaton (CR) n SRC s gnored by most lterature. Ths paper [Zhang, Yang and Feng (0)] devoted to analyze the workng mechansm of SRC, and ndcated that t was the CR but not the l -norm sparsty that made SRC powerful for face classfcaton. The authors proposed a very smple yet much more effcent face classfcaton scheme, namely CR based classfcaton wth regularzed least square (CRC_RLS), whch had very compettve classfcaton results, many classc and contemporary face recognton algorthms work well on publc data sets, but degrade sharply when they are used n a real recognton system. Ths s mostly due to the dffculty of smultaneously handlng varatons n llumnaton, mage msalgnment, and occluson n the test mage. Consderng ths problem, Wagner et al. [Wagner, Wrght, Ganesh et al. (0)] proposed a conceptually smple face recognton system that acheved a hgh degree of robustness and stablty to llumnaton varaton, mage msalgnment, and partal occluson. Besdes, Zhang et al. [Zhang, Zhang, Huang et al. (03)] proposed a pose-robust face recognton method to handle the challengng task of face recognton n the presence of large pose dfference between gallery and probe faces. The proposed method exploted the sparse property of the representaton coeffcents of a face mage over ts correspondng vew-dctonary. In hyperspectral mage classfcaton, Tang et al. [Tang, Chen, Lu et al. (05)] present a hyperspectral mage classfcaton method based on sparse representaton and superpxel segmentaton. By refnng the spectral classfcaton results wth the spatal constrants, the accuracy of classfcaton s mproved by a substantal margn n Tang et al. [Tang, Chen, Lu et al. (05)]. Notng that the structural nformaton can earn some extra dscrmnaton for the classfcaton framework [Lu, Fu and He (07)], some methods consderng the structural and contextual nformaton are presented. A new sparsty-based algorthm for the classfcaton of hyperspectral magery was proposed n Chen et al. [Chen, Nasrabad and Tran (0)], whch reled on the observaton that a hyperspectral pxel could be sparsely represented by a lnear combnaton of a few tranng samples from a structured dctonary. They manly used Laplacan constrant and jont sparsty model to ncorporate the contextual nformaton nto the sparse recovery optmzaton problem n order to mprove the classfcaton performance. To overcome ths problem

3 Weghted Sparse Image Classfcaton Based on Low Rank Representaton 93 that the sparse representaton-based classfcaton (SRC) methods gnore the sparse representaton resduals (.e. outlers), L et al. [L, Ma, Me et al. (07)] proposed a robust SRC (RSRC) method whch could handle outlers. They extended the RSRC to the jont robust sparsty model named JRSRC, where pxels n a small neghborhood around the test pxel were smultaneously represented by lnear combnatons of a few tranng samples and outlers. A superpxel tensor sparse codng (STSC) based hyperspectral mage classfcaton (HIC) method s proposed, by explorng the hgh-order structure of hyperspectral mage and utlzng nformaton along all dmensons to better understand data n Feng et al. [Feng, Wang, Yang et al. (07)]. Artcle [Sun, Qu, Nasrabad et al. (04)] proposes a new structured pror called the low-rank (LR) group pror, whch can be consdered as a modfcaton of the LR pror. Structured Prors for Sparse- Representaton-Based Hyperspectral Image Classfcaton. The paper [Zhang, Song, Gao et al. (06)] presents a new spectral spatal feature learnng method for hyperspectral mage classfcaton, whch ntegrates spectral and Zeng et al. [Zeng, L, Lang et al. (00)] spatal nformaton nto group sparse codng (GSC) va clusters and propose a novel kernelzed classfcaton framework based on sparse representaton consderng the mage classfcaton problem based on the smlartes between mages [Zhang, Zhang, Lu et al. (05)]. Artcle [Zeng, L, Lang et al. (00)] proposes a fast jont sparse representaton classfcaton method wth mult-feature combnaton learnng for hyperspectral magery and ncorporate contextual neghborhood nformaton of the mage nto each knd of feature to further mprove the classfcaton performance. The paper [Wang, Xe, L et al. (05)] nvestgates STDA (Sparse Tensor Dscrmnant Analyss) for feature extracton and t s the frst tme that STDA s appled for HIS (Hyperspectral magery) and attempts to adopt STDA to preserve useful structural nformaton n the orgnal data and obtan multple nterrelated sparse dscrmnant subspaces. In remote sensng mage classfcaton,the paper [Shvakumar, Natarajan and Murthy (05)] presents a novel mult-kernel based sparse representaton for the classfcaton of Remotely sensed mages. The sparse representaton based feature extracton are n a run whch s a sgnal dependent feature extracton and thus more accurate. The paper [Song, L, Dalla et al. (04)] proposes to explot sparse representatons of morphologcal attrbute profles for remotely sensed mage classfcaton. By usng the sparse representaton classfcaton framework to explot ths characterstc of the EMAPs. Wth more and more sources of mage data on the Internet, mages are becomng more and more cluttered, makng more and more mages lack complete category nformaton. Based on ths, the researchers proposed sem-supervsed and unsupervsed mage classfcaton methods. To address the problem of face recognton when there s only few, or even only a sngle, labeled examples of the face that we wsh to recognze. The man dea was that: they used the varaton dctonary to characterze the lnear nusance varables va the sparsty framework and prototype face mages were estmated as a gallery dctonary va a Gaussan mxture model, wth mxed labeled and unlabeled samples n a sem-supervsed manner, to deal wth the non-lnear nusance varatons between labeled and unlabeled samples. Unsupervsed learnng methods for buldng feature extractors have a long and successful hstory n pattern recognton and computer vson. Document [Huang, Boureau and Le (007)] proposes an unsupervsed method to learn the sparse feature detector herarchy, whch s nvarant for small shfts and

4 94 Copyrght 08 Tech Scence Press CMC, vol.56, no., pp.9-05, 08 dstortons. Artcle [Zeler, Krshnan, Taylor et al. (00)] present a learnng framework where features that capture these md-level cues spontaneously emerge from mage data and the approach s based on the convolutonal decomposton of mages under a sparsty constrant and s totally unsupervsed. The paper [Poultney, Chopra and Cun (007)] descrbes a novel unsupervsed method for learnng sparse, overcomplete features. The model uses a lnear encoder, and a lnear decoder preceded by a sparsfyng non-lnearty that turns a code vector nto a quas-bnary sparse code vector. The major contrbuton of paper [Hassar, Ejbal and Zaed (06)] s to show how to extract features and tran an mage classfcaton system on large-scale datasets. In ths paper, we proposed novel sparse representaton-based mage classfcaton wth weghted supervson sparse codng. It frstly constructed the supervson coeffcent wth Low rank representaton, whch would help to mne the structural nformaton hdden n the data. And then, the supervson coeffcent s ncorporated nto a weghted sparse representaton framework to preserve the codng structure of smlar samples. It s verfed that the proposed method shows some advantage on the publc test dataset. The remanng of the paper s arranged as follows. In secton II, several smlar prevous works are analyzed. In secton III, the proposed method s descrbed n detal. In secton IV, the expermental results are shown to demonstrate the superorty of the proposed method. Secton V concludes the paper. Related work Although the tradtonal spatal pyramd matchng (SPM) approach works well for mage classfcaton, people emprcally found that, to acheve good performance, tradtonal SPM has to use classfers wth nonlnear Mercer kernels. Accordngly, the nonlnear classfer has to afford addtonal computatonal complexty, bearng O(n3) n tranng and O(n) for testng n SVM, where n s the number of support vectors. Ths mples a poor scalablty of the SPM approach for real applcatons. To mprove the scalablty, researchers am at obtanng nonlnear feature representatons that work better wth lnear classfers Let X be a set of D-dmensonal local descrptors extracted from an mage, D N. e. X x, x,..., x R D M B = b, b,..., b R, =. Gven a codebook wth M entres, N dfferent codng schemes convert each descrptor nto admensonal code to generate the fnal mage representaton. Ths secton revews three exstng codng schemes.. Codng descrptors n VQ Tradtonal SPM uses VQ codng whch solves the followng constraned least square fttng problem: arg mn C N x Bc () = s. t. c =, c 0, where C c c c =,,..., N s the set of codes for X. The cardnalty constrant c 0 = M

5 Weghted Sparse Image Classfcaton Based on Low Rank Representaton 95 means that there wll be only one non-zero element n each code c, correspondng to the quantzaton d of x.the non-negatve, constrant c =, c 0 means that the codng weght for x s. In practce, the sngle non-zero element s found by searchng the nearest neghbor.. Codng descrptors n ScSPM To amelorate the quantzaton loss of VQ, the restrctve cardnalty constrant c 0 = n Eq. () can be relaxed by usng a sparsty regularzaton term. In ScSPM [Yang, Yu, Gong et al. (009)], such a sparsty regularzaton term s selected to be the norm of c, and codng each local descrptor x thus becomes a standard sparse codng (SC) [Lee, Battle, Rana et al. (007)] problem: arg mn C N x Bc + c () = The sparsty regularzaton term plays several mportant roles: Frst, the codebook B s usually over-complete,.. e M D, and hence regularzaton s necessary to ensure that the under-determned system has a unque soluton ; Second, the sparsty pror allows the learned representaton to capture salent patterns of local descrptors; Thrd, the sparse codng can acheve much less quantzaton error than VQ. Accordngly, even wth lnear SVM classfer, ScSPM can outperform the nonlnear SPM approach by a large margn on benchmarks lke Caltech-0 [Yang, Yu, Gong et al. (009)]..3 Codng descrptors n LLC Localty-constraned Lnear Codng (LLC) was presented by Wang et al. [Wang, Yang, Yu et al. (00)]. LLC ncorporates localty constrant nstead of the sparsty constrant n Eq., whch leads to several favorable propertes, ncludng better reconstructon, local smooth sparsty and analytcal soluton. Specfcally, the LLC code uses the followng crtera [Yuan, Ma and Yulle (07)]: C N + λ (3) = (4) M denotes the element-wse multplcaton, and d mn x Bc d c s. t. c =, where s the localty adaptor that gves dfferent freedom for each bass vector proportonal to ts smlarty to the nput descrptor x. Specfcally, ( ) dst x,b d = exp σ T = M, and dst ( x,b ) where dst ( x,b) dst ( x,b ),,dst ( x,b ) (5) j s the Eucldean dstance between x and b j. s used for adjustng the weght decay speed for the

6 96 Copyrght 08 Tech Scence Press CMC, vol.56, no., pp.9-05, 08 localty adaptor. Usually we further normalze d to be between (0, ) by subtractng ( ( )) from dst ( x,b) max dst x,b. The constrant c = follows the shft-nvarant requrements of the LLC code. Note that the LLC code n Eq. (5) s not sparse n the sense of l 0 norm, but s sparse n the sense that the soluton only has few sgnfcant values. In practce, we smply threshold those small coeffcents to be zero. Wth the above descrpton of LLC codng, we can see that the localty constran wll earn extra dscrmnaton for the codng coeffcents. Because, some structure nformaton s ntroduced the codng by enforcng some coeffcents wth weak sample correlaton to be zero, whch wll help to select more samples wthn the same subspace. Next, we wll proposed a weghted sparse classfcaton framework to mprove the codng structure. And then, to explore the supervson nformaton hdden n the data, a novel supervson constrant tem about codng approxmaton are also proposed as the part of the weghted sparse classfcaton framework. 3 Sparse mage classfcaton model based on low-rank supervson 3. Low-rank representaton model Low-rank matrx recovery s the development and promoton of the compressve sensng theory, usng the rank as a measure of the matrx sparseness. The low-rank representaton model has well capable of handlng hgh-dmensonal sgnal data. The model can be used to recover damaged observatonal samples and can fnd low-dmensonal feature space from nosy samples. A matrx representaton of the mage data, the orgnal observaton m n data matrx X R and the model that uses the rank of matrx for sparse representaton s as follows: mn rank( X ) st.. ( X) = b (6) X where rank () s the rank of the matrx, () s a lnear mappng functon from m n p orgnal data matrx to observed varable, namely R R and b R p. In the model, we get a low-rank constrant on matrx X. However, snce the functon rank() n the model equaton s dscrete and non-convex, solvng model s an NP-Hard problem. In order to solve such problem, t s a common practce to convert ths NP-Hard combnatoral optmzaton problem to correspondng convex optmzaton problems by transformng some objectve functon to some convex functon. rank() can also represent the number of non-zero sngular values n the matrx, so we can consder mn rank( X ) s a l 0 -norm constrant problem of matrx sngular value. That s to say, mnmzng the l - 0 norm of vectors s to mnmze the rank of the matrx. Therefore, the soluton of mnmzng matrx rank can refer to the relevant deas and methods for solvng the mnmum l 0 -norm. If the sample matrx X exsts n several low-dmensonal spaces, the sample matrx X can be lnearly represented by a set of low-dmensonal space bases A, that s, the sample tself s selected as the dctonary, the lower rank represents the coeffcent matrx Z, and the Z represents each data vector The weght of a lnear combnaton. A low-rank

7 Weghted Sparse Image Classfcaton Based on Low Rank Representaton 97 constrant on the coeffcent Z results n a low-rank representaton of the sample matrx X as follows: mn rank( Z ) st.. X = XZ (7) Z whch s a non-convex optmzaton problem. In the soluton, we usually apply convexrelaxaton method and replace rank( Z ) wth the matrx kernel functon Z. The * followng formula: mn Z Z st.. X = XZ (8) * In practcal applcatons, the sgnal s lkely to be polluted by nose, so the above equaton can be further expressed as: mn ZE, Z + λ E st.. X = XZ + E (9) *, where, s called l, -norm, λ s the regularzaton parameter, E s the resdual. For dfferent types of nose, the l, -norm has strong processng power. In recent years, researchers have proposed many effcent optmzaton algorthms to solve the above problems, such as Iteratve Thresholdng, Exact Augmented Lagrange Multpler, Inexact Augmented Lagrange Multpler and so on. These algorthms can learn from l -norm mnmzaton, the followng descrbes the Exact and Inexact Augmented Lagrange Multpler algorthm. Before that, we need Augmented Lagrange Multpler (ALM) algorthm. The objectve functon for a constraned optmzaton problem can be descrbed by: mn f( X ) st.. hx ( ) = 0 (0) where f n s a convex functon, whch represents mappng from R to R. h represents n mappng from R to m R. Then the defnton of Augmented Lagrange Multpler functon s as follows: μ L( X, Y, μ) = f ( X ) + Y, h( X ) + h( X ) () F where Y s Lagrange multpler. μ s known as the penalty coeffcent that s a postve number. s nner product operator. When the values of Y and are approprate, the objectve functon can be solved by Augmented Lagrange algorthm. Asume that X = ( A, E), f ( X ) = A + λ E *, h( X ) = D A E. The Eq. () can be expressed by ths: μ L( A, E, Y, μ) = A + λ E + Y, D A E + D A E () * F whch can be solved by usng alternate ways to optmze the update. Let Y and E be fxed values solvng mnmzed L to obtan A. Then fx Y and A, and solve for mnmzed L to obtan E. It s done teratvely untl the convergent soluton s eventually obtaned that s called the Exact Augmented Lagrange Multpler method. Snce A and E are coupled to each other n Eq. (), each teraton wll be placed n the

8 98 Copyrght 08 Tech Scence Press CMC, vol.56, no., pp.9-05, 08 same sub-problem durng the teraton, whch makes the soluton feasble. In practce the Exact Augmented Lagrange Multpler method requres multple teratons, so the algorthm runs at a lower speed. On the bass of the former, an Inexact Augmented Lagrange Multpler method s proposed, n whch the A and E are updated once at each teraton to obtan the approxmate soluton of the sub-problem. Fgure : Ideal structure of the coeffcent matrx n SRC The core dea based on sparse representaton s that the test sample s expressed by a lnear combnaton of tranng samples. Because most non-zero elements have the same base correspondng to the test sample. In deal case, we expect each sample to be n ts own category subspace and all the category subspaces do not overlap. Specfcally, gven a category of mages recorded as C and dctonares D = [ D,..., D C ] whch D C contans tranng samples from the category c=,..., C. That s meanng that a new sample y c belongng to the category c c can be represented by y Dc a, a s a representaton coeffcent under a sub-dctonary D. So we can use the dctonary D to represent y : c = c C c c c. Most of the vald elements should be located n c y Da D a D a D a a, so the coeffcent vector a should be sparse. From vector to matrx form, Y = [ Y,..., Yc,..., YC] s the entre sample set matrx contanng the category samples, the coeffcent matrx A wll be also sparse, and n the deal case the matrx A s a block dagonal matrx as shown n Fg.. 3. Correlaton matrx constructon Assume that the test sample matrx Y = [ y, y,..., y n ], y n denotes the no. n test sample vector. Based on above analyss, we can use the sample as a dctonary and use the matrx Z to explore the correlaton between samples to obtan the low-rank representaton model of the test sample as follows: mn ZE, Z + λ E st.. Y = YZ + E (3) * where s kernel functon, * E s resdual and λ s regularzaton parameters. Eq. 3 can be solved usng the Augmented Lagrange Multpler method whch s ntroduced earler to obtan a low-rank representaton matrx Z for Y. Z contans some sample features.

9 Weghted Sparse Image Classfcaton Based on Low Rank Representaton Sparse mage classfcaton model based on low-rank supervson To make better use of correlatons between samples and obtan feature representatons wth better dscrmnaton capablty, we use the low-rank representaton matrx Z to perform low-rank supervson constrants on the sparse codng process and propose a new low-rank supervsed sparse codng model. Frst, we can obtan a supervsory matrx from a low-rank representaton matrx, as shown n the followng equaton: T Z + Z W = (4) where represents the absolute value of each element n the matrx. Let the category- m m known sample matrx X = [ X, X,..., X k ] and Xk = [ xk, xk,..., xk ]. xk represents the m th sample vector belongng to the category number k. Usng a self-descrbng category-known sample as a dctonary, we can get a new sparse codng model as follows: mn Y XA + λ P A + η A Aj Wj F (5) A j where A s feature representaton matrx, λ and η are regularzaton parameters. In the above model, we have added the supervson constrant tem A A j j Wj to ncrease the dfference n codng between dfferent categores, where and j are the column numbers of the feature representaton matrx A. P s the correlated weghted for the sparse coeffcent. P exp j y Dj =. denotes the element-wse multplcaton operator. W j s used to represent the elements of the row and column j n the supervsng matrx W. By solvng the model 0, we can get the representaton matrx A wth stronger dscrmnaton ablty. After obtanng the feature representaton matrx A, the reconstructon error can be used to classfy and the classfcaton model as follows: = arg mn y X A (6) k k k where k {,,..., n}, A k s the feature code that represents the k th column n the matrx A correspondng to the th sample. Fnd the Eq. (6) to mnmze the reconstructon error label s the classfcaton result, that s the formula for the mnmum value of k. 4 Solvng the sparse mage classfcaton model based on low-rank supervson Ths secton descrbes the process of solvng the above low-rank supervsed codng model n detal. The model 0 can be transformed as follows: P ( A ) = F j j j Y XA + λ P A + η A A W (7) Eq. 7 s a non-convex problem. We can make an equdstant transformaton to get the T followng based on A Aj Wj = trace( ALA ): j

10 00 Copyrght 08 Tech Scence Press CMC, vol.56, no., pp.9-05, 08 T P( A) = Y XA + λ P A + ηtrace( ALA ) (8) F where trace () s trace of matrx, L s lagrange operator and L = D W. The matrx D s a dagonal matrx whose elements on the dagonal correspond to the sum of all elements of the column vector n the matrx W, namely D = Wj, and j are the row and column numbers of the matrx. Ths problem s transformed nto a convex optmzaton problem. T Let G( A) = Y XA + ηtrace( ALA ) and H( A) = λ P A, then Eq. (8) can be F replaced wth the followng form: P( A) = G( A) + H( A) (9) For the optmzaton soluton, we can get the gradent soluton formula of GA ( ) as follows: ( ) T T G A = X ( Y XA) + ηal (0) where s a gradent ndcator. Accordng to Eq. (9) and Eq. (0), the teratve shrnkng algorthm can be used to solve the orgnal model (7), whch teratve soluton s as follows: k ( ) ( ) k A arg mn A G A H A F + = + () As for the Eq. (), t s a typcal weghted l -norm mnmzaton problem, whch can be solved wth the numercal method n Guleryuz [Guleryuz (006)]. And then, we can obtan the feature representaton matrx A and use the classfcaton model shown n model (6) to classfy mages. 5 Expermental results and analyss 5. Expermental data For the weghted sparse mage classfcaton method based on low-rank representaton proposed n ths paper, we take the ORL and COIL-0 mage datasets as the expermental datasets. The ORL face dataset contans 400 face mages, whch were shot by 0 people under dfferent lghtng condtons, varyng vew and expressons. Each person has about 0 face mages. Fg. shows some face samples of the ORL dataset. j Fgure : Two groups of face samples of ORL dataset

11 Weghted Sparse Image Classfcaton Based on Low Rank Representaton 0 The COIL-0 mage dataset s collected by Columba Object Image Lbrary, whch contans mages of 0 tems. Durng shootng the mage, the object s placed on a rotatng plate wth black background. Through the 360 degree rotaton of the plate to change the atttude of the tem relatve to the camera. Each object n the dataset has 7 mages wth dfferent angles, and some examples are shown n Fg. 3. Fgure 3: Example mages of COIL-0 database In the experment, we mplemented the sparse representaton-based mage classfcaton methods SRC, CRC, LRSRC on the above two publc datasets. The algorthm proposed n ths paper s compared to verfy. 5. Comparson and analyss of experments Frst of all, n order to verfy the valdty of the method proposed n ths chapter, we use the ORL face mage data set to dsplay, and vsualze the obtaned low-rank representaton matrx and ts correspondng feature representaton matrx. The low-rank representaton matrx s shown n Fg. 4, and the characterstc representaton matrx s shown n Fg. 5. From these two fgures, t can be observed that the representaton matrx has a dstnct dagonal block structure, ndcatng that the representaton matrx should theoretcally have the dscrmnatve ablty of classfcaton, the expermental result of the latter also confrmed ths predcton. From the comparson of these two graphs, we can also fnd that compared wth the low rank representaton matrx, the elements n the dagonal matrx of the representaton matrx are enhanced after beng coded from the supervson lmt to make t have a more obvous dagonal block structure, ndcatng better class resoluton. Fgure 4: Vsualzaton of low-rank representaton matrx for ORL

12 0 Copyrght 08 Tech Scence Press CMC, vol.56, no., pp.9-05, 08 Fgure 5: Vsualzaton of sparse representaton matrx for ORL We performed smulaton experments on the above methods n the Extended YaleB face mage dataset and COIL-0 mage dataset and obtaned the correspondng expermental results. We test fve tmes for each method, and take the average accuracy as the fnal result, whch s shown n Tab.. The number shown n the parentheses denotes the number of tranng samples. Table : Average accuracy of each classfcaton method ORL(5) COIL-0(30) SRC % % CRC % % LRSRC % % Proposed Method % % From Tab., we can see that our proposed method shows hgher accuracy classfcaton result on all the expermental datasets over the comparson methods. It s verfed that the weghted sparse codng wth the low rank supervson can greatly mprove the structure of codng to be more dscrmnatve. 6 Summary On the bass of the SRC method, ths paper proposes a weghted sparse mage classfcaton method based on low-rank supervson. The proposed one strengthens the sample dscrmnaton ablty of the feature representaton matrx, whch makes full use of the correlaton between samples to weghted code the mage sparsely. Dfferent types of sparse represent the degree of codng dscrmnaton, whch s beleved to mprove the accuracy of mage classfcaton. We replace the non-convex terms n the model equvalently, use the teratve shrnkng algorthm to solve and verfy the correctness through some experments. Compared wth related conventonal classfcaton methods, the method proposed n ths paper s better than them.

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