Abstract The original dataset is decomposed into a set of representative bases with corresponding sparse errors for modeling the raw data in standard low-rank matrix recovery algorithm. Inspired by the Fisher criterion, a low-rank matrix recovery algorithm based on Fisher discriminate criterion is presented in this paper. Low-rank matrix recovery is executed in a supervised learning mode, i.e., taking the within-class scatter and between-class scatter into account when the whole label information is available. The proposed model can be solved by the augmented Lagrange multipliers, and the additional discriminating ability is provided to the standard low-rank models for improving performance. The representative bases learned by the proposed algorithm are encouraged to be structurally coherent within the same class and be independent between classes as much as possible. Numerical simulations on face recognition tasks demonstrate that the proposed algorithm is competitive with the state-of-the-art alternatives.
[1] Olshausen B A, Field D J. Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1? Vision Research, 1997, 37(23): 3311-3325 [2] Vinje W E, Gallant J L. Sparse Coding and Decorrelation in Primary Visual Cortex During Natural Vision. Science, 2000, 287(5456): 1273-1276 [3] Wright J, Ma Y, Mairal J, et al. Sparse Representation for Computer Vision and Pattern Recognition. Proceedings of the IEEE, 2010, 98(6): 1031-1044 [4] Wagner A, Wright J, Ganesh A, et al. Towards a Practical Face Re-cognition System: Robust Registration and Illumination by Sparse Representation. IEEE Trans on Pattern Analysis and Machine Intelligence, 2012, 34(2): 372-386 [5] Yang M, Zhang D, Yang J, et al. Robust Sparse Coding for Face Recognition // Proc of the 24th IEEE Conference on Computer Vision and Pattern Recognition. Providence, USA, 2011: 625-632 [6] Turk M, Pentland A. Eigenfaces for Recognition. Journal of Cognitive Neuroscience, 1991, 3(1): 71-86 [7] Belhumeur P N, Hespanha J P, Kriegman D J. Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection. IEEE Trans on Pattern Analysis and Machine Intelligence, 1997, 19(7): 711-720 [8] He X F, Yan S C, Hu Y X, et al. Face Recognition Using Laplacianfaces. IEEE Trans on Pattern Analysis and Machine Intelligence, 2005, 27(3): 328-340 [9] He X F, Niyogi P. Locality Preserving Projections.[EB/OL].[2014-02-20]. http://papers.nips.cc/paper/2359-locality-preserving-projections.pdf [10] Cai D, He X F, Han J W, et al. Orthogonal Laplacianfaces for Face Recognition. IEEE Trans on Image Processing, 2006, 15(11): 3608-3614 [11] Candès E J, Recht B. Exact Low Rank Matrix Completion via Convex optimization // Proc of the 46th Annual Allerton Conference on Communication, Control, and Computing. Urbana-Champaign, USA, 2008: 806-812 [12] Lin Z C, Chen M M, Ma Y. The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrix[EB/OL].[2014-02-20]. http://www.cis.pku.edu.cn/faculty/vision/zlin/Publications/ALM-v5.pdf [13] Wright J, Yang A Y, Ganesh A, et al. Robust Face Recognition via Sparse Representation. IEEE Trans on Pattern Analysis and Machine Intelligence, 2009, 31(2): 210-227
2015, Vol. 28 
