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Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

CN 10-1014/TP

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2018 Impact Factor: 1.129

Front. Comput. Sci.    2020, Vol. 14 Issue (4) : 144306    https://doi.org/10.1007/s11704-019-7200-y
RESEARCH ARTICLE
Adaptive sparse and dense hybrid representation with nonconvex optimization
Xuejun WANG1, Feilong CAO2, Wenjian WANG3()
1. School of Computer Science and Technology, Shanxi University, Taiyuan 030006, China
2. School of Science, China Jiliang University, Hangzhou 310018, China
3. Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Taiyuan 030006, China
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Abstract

Sparse representation has been widely used in signal processing, pattern recognition and computer vision etc. Excellent achievements have been made in both theoretical researches and practical applications. However, there are two limitations on the application of classification. One is that sufficient training samples are required for each class, and the other is that samples should be uncorrupted. In order to alleviate above problems, a sparse and dense hybrid representation (SDR) framework has been proposed, where the training dictionary is decomposed into a class-specific dictionary and a non-class-specific dictionary. SDR puts 1 constraint on the coefficients of class-specific dictionary. Nevertheless, it over-emphasizes the sparsity and overlooks the correlation information in class-specific dictionary, which may lead to poor classification results. To overcome this disadvantage, an adaptive sparse and dense hybrid representation with nonconvex optimization (ASDR-NO) is proposed in this paper. The trace norm is adopted in class-specific dictionary, which is different from general approaches. By doing so, the dictionary structure becomes adaptive and the representationability of the dictionary will be improved. Meanwhile, a nonconvex surrogate is used to approximate the rank function in dictionary decomposition in order to avoid a suboptimal solution of the original rank minimization, which can be solved by iteratively reweighted nuclear norm (IRNN) algorithm. Extensive experiments conducted on benchmark data sets have verified the effectiveness and advancement of the proposed algorithm compared with the state-of-the-art sparse representation methods.

Keywords sparse representation      trace norm      nonconvex optimization      low rank matrix recovery      iteratively reweighted nuclear norm     
Corresponding Author(s): Wenjian WANG   
Just Accepted Date: 24 July 2019   Issue Date: 11 March 2020
 Cite this article:   
Xuejun WANG,Feilong CAO,Wenjian WANG. Adaptive sparse and dense hybrid representation with nonconvex optimization[J]. Front. Comput. Sci., 2020, 14(4): 144306.
 URL:  
https://academic.hep.com.cn/fcs/EN/10.1007/s11704-019-7200-y
https://academic.hep.com.cn/fcs/EN/Y2020/V14/I4/144306
1 B K Natarajan. Sparse approximate solutions to linear systems. Siam Journal on Computing, 1995, 24(2): 227–234
https://doi.org/10.1137/S0097539792240406
2 M Huang, W Yang, J Jiang, Y Wu, Y Zhang, W Chen, Q Feng. Brain extraction based on locally linear representation-based classification. Neuroimage, 2014, 92(10): 322–339
https://doi.org/10.1016/j.neuroimage.2014.01.059
3 D L Donoho. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306
https://doi.org/10.1109/TIT.2006.871582
4 E J Candès, J Romberg, T Tao. Robust uncertainty principles: exact signal frequency information. IEEE Transactions on Information Theory, 2006, 52(2): 489–509
https://doi.org/10.1109/TIT.2005.862083
5 M Elad, M A T Figueiredo, Y Ma. On the role of sparse and redundant representations in image processing. Proceedings of the IEEE, 2010, 98(6): 972–982
https://doi.org/10.1109/JPROC.2009.2037655
6 M Elad. Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. 1st ed. New York: Springer Science and Business Media, 2010
https://doi.org/10.1007/978-1-4419-7011-4
7 A M Bruckstein, D L Donoho, M Elad. From sparse solutions of systems of equations to sparse modeling of signals and images. Siam Review, 2009, 51(1): 34–81
https://doi.org/10.1137/060657704
8 J Wright, Y Ma, J Mairal, G Sapiro, T S Huang, S Yan. Sparse representation for computer vision and pattern recognition. Proceedings of the IEEE, 2010, 98(6): 1031–1044
https://doi.org/10.1109/JPROC.2010.2044470
9 E Candès, J Romberg. Sparsity and incoherence in compressive sampling. Inverse Problems, 2006, 23(3): 969–985
https://doi.org/10.1088/0266-5611/23/3/008
10 J Wright, A Y Yang, A Ganesh, S S Sastry, Y Ma. Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(2): 210–227
https://doi.org/10.1109/TPAMI.2008.79
11 T Cover, P Hart. Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 2002, 13(1): 21–27
https://doi.org/10.1109/TIT.1967.1053964
12 S Li, J Lu. Face recognition using the nearest feature line method. IEEETransactions on Neural Networks, 1999, 10(2): 439–443
https://doi.org/10.1109/72.750575
13 J T Chien, C C Wu. Discriminant waveletfaces and nearest feature classifiers for face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 24(12): 1644–1649
https://doi.org/10.1109/TPAMI.2002.1114855
14 K C Lee, J Ho, D J Kriegman. Acquiring linear subspaces for face recognition under variable lighting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(5): 684–698
https://doi.org/10.1109/TPAMI.2005.92
15 Y Xu, Q Zhu, Z Fan, D Zhang, J Mi, Z Lai. Using the idea of the sparse representation to perform coarse-to-fine face recognition. Information Sciences, 2013, 238(7): 138–148
https://doi.org/10.1016/j.ins.2013.02.051
16 M Yang, L Zhang. Gabor feature based sparse representation for face recognition with gabor occlusion dictionary. In: Proceedings of European Conference on Computer Vision. 2010, 448–461
https://doi.org/10.1007/978-3-642-15567-3_33
17 J Wang, J Yang, K Yu, F Lv, T Huang, Y Gong. Locality-constrained linear coding for image classification. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2010, 3360–3367
https://doi.org/10.1109/CVPR.2010.5540018
18 R He, W S Zheng, B G Hu. Maximum correntropy criterion for robust face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 33(8): 1561–1576
https://doi.org/10.1109/TPAMI.2010.220
19 A Wagner, J Wright, A Ganesh, Z Zhou, H Mobahi, Y Ma. Toward a practical face recognition system: robust alignment and illumination by sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 34(2): 372–386
https://doi.org/10.1109/TPAMI.2011.112
20 X Wang, M Yang, L Shen. Structured regularized robust coding for face recognition. IEEE Transactions on Image Processing, 2013, 22(5): 1753–1766
https://doi.org/10.1109/TIP.2012.2235849
21 Y Xu, Z Zhong, J Yang, J You, D Zhang. A new discriminative sparse representation method for robust face recognition via l2 regularization. IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(10): 2233–2242
https://doi.org/10.1109/TNNLS.2016.2580572
22 L Zhang, M Yang. Sparse representation or collaborative representation: which helps face recognition? In: Proceedings of IEEE Interna tional Conference on Computer Vision. 2012, 471–478
23 J Wang, C Lu, M Wang, P Li, S Yan, X Hu. Robust face recognition via adaptive sparse representation. IEEE Transactions on Cybernetics, 2014, 44(12): 2368–2378
https://doi.org/10.1109/TCYB.2014.2307067
24 E Grave, G Obozinski, F Bach. Trace lasso: a trace norm regularization for correlated designs. In: Proceedings of the 24th International Conference on Neural Information Processing Systems. 2011, 2187–2195
25 E J Candès, X Li, Y Ma, J Wright. Robust principal component analysis? Journal of the ACM, 2009, 58(3): 1101–1137
https://doi.org/10.1145/1970392.1970395
26 Y C F Wang, C P Wei, C F Chen. Low-rank matrix recovery with structural incoherence for robust face recognition. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2012, 2618–2625
27 L Ma, C Wang, B Xiao, W Zhou. Sparse representation for face recognition based on discriminative low-rank dictionary learning. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2012, 2586–2593
28 Y Zhang, Z Jiang, L S Davis. Learning structured low-rank representations for image classification. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2013, 676–683
https://doi.org/10.1109/CVPR.2013.93
29 W Deng, J Hu, J Guo. Extended SRC: undersampled face recognition via intraclass variant dictionary. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 34(9): 1864–1870
https://doi.org/10.1109/TPAMI.2012.30
30 X Jiang, J Lai. Sparse and dense hybrid representation via dictionary decomposition for face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 37(5): 1067–1079
https://doi.org/10.1109/TPAMI.2014.2359453
31 Y Yang, Z Ma, A G Hauptmann, N Sebe. Feature selection for multimedia analysis by sharing information among multiple tasks. IEEE Transactions on Multimedia, 2013, 15(3): 661–669
https://doi.org/10.1109/TMM.2012.2237023
32 J Trzasko, A Manduca. Highly undersampled magnetic resonance image reconstruction via homotopic ℓ0-minimization. IEEE Transactions on Medical Imaging, 2009, 28(1): 106–121
https://doi.org/10.1109/TMI.2008.927346
33 W Deng, J Hu, J Guo. In defense of sparsity based face recognition. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2013, 399–406
https://doi.org/10.1109/CVPR.2013.58
34 D L Donoho. For most large underdetermined systems of linear equations the minimal ℓ1-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics, 2010, 59(6): 797–829
https://doi.org/10.1002/cpa.20132
35 E J Candès, J K Romberg, T Tao. Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics, 2005, 59(8): 1207–1223
https://doi.org/10.1002/cpa.20124
36 Z Lin, M Chen, Y Ma. The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. 2010, arXiv preprint arXiv:1009.5055
37 H Zou, T Hastie. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, 2005, 67(2): 301–320
https://doi.org/10.1111/j.1467-9868.2005.00503.x
38 J F Cai, E J Candès, Z Shen. A singular value thresholding algorithm for matrix completion. Siam Journal on Optimization, 2010, 20(4): 1956–1982
https://doi.org/10.1137/080738970
39 E T Hale, W Yin, Y Zhang. Fixed-point continuation for ℓ1- minimization: methodology and convergence. Siam Journal on Optimization, 2008, 19(3): 1107–1130
https://doi.org/10.1137/070698920
40 C Lu, J Tang, S Yan, Z Lin. Nonconvex nonsmooth low rank minimization via iteratively reweighted nuclear norm. IEEE Transactions Image Process, 2016, 25(2): 829–839
https://doi.org/10.1109/TIP.2015.2511584
41 P J Phillips, H Wechsler, J Huang, P J Rauss. The feret database and evaluation procedure for face-recognition algorithms. Image and Vision Computing, 1998, 16(5): 295–306
https://doi.org/10.1016/S0262-8856(97)00070-X
42 F S Samaria, A C Harter. Parameterisation of a stochastic model for human face identification. In: Proceedings of IEEE Workshop on Applications of Computer Vision. 1994, 138–142
43 M Hollander, D A Wolfe, E Chicken. Nonparametric Statistical Methods. 3rd ed. New York: Wiley, 1999
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