Abstract
For the low-rank representation-based subspace clustering, the affinity matrix is block diagonal. In this paper, a novel robust discriminant low-rank representation (RDLRR) algorithm is proposed to enhance the block diagonal property to explore the multiple subspace structures of samples. In order to cluster samples into their corresponding subspace and remove outliers, the proposed RDLRR considers both the within-class and the between-class distance during seeking the lowest-rank representation of samples. RDLRR could well indicate the global structure of samples, when the labeling is available. We conduct experiments on several datasets, including the Extended Yale B, AR and Hopkins 155, to show that our approach outperforms all the other state-of-the-art approaches.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Candès EJ, Li X, Ma Y, Wright J (2011) Robust principal component analysis? JACM 58(3):11
Chen J, Yi Z (2014) Sparse representation for face recognition by discriminative low-rank matrix recovery. J Vis Commun Image Represent 25(5):763–773
Elhamifar E, Vidal R (2009) Sparse subspace clustering. In: IEEE conference on computer vision and pattern recognition, 2009, CVPR 2009, pp 2790–2797
Elhamifar E, Vidal R (2013) Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781
Li B, Zhang Y, Lin Z, Lu H (2015) Subspace clustering by mixture of gaussian regression. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 2094–2102
Lin Z, Chen M, Ma Y (2010) The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. arXiv preprint arXiv:1009.5055
Liu G, Yan S (2011) Latent low-rank representation for subspace segmentation and feature extraction. In: 2011 IEEE international conference on computer vision (ICCV), pp 1615–1622
Liu G, Yan S (2014) Latent low-rank representation. In: Fu Y (ed) Low-rank and sparse modeling for visual analysis. Springer, Cham
Liu G, Lin Z, Yu Y (2010) Robust subspace segmentation by low-rank representation. In: Proceedings of the 27th international conference on machine learning (ICML-10), pp 663–670
Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2013) Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell 35(1):171–184
Lu C, Lin Z, Yan S (2015) Smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization. IEEE Trans Image Process 24(2):646–654
Lvd Maaten, Hinton G (2008) Visualizing data using t-sne. J Mach Learn Res 9:2579–2605
Duda O, Hart P, Stork DG (2000) Pattern classification. Wiley, Hoboken
Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905
Vidal R (2011) Subspace clustering. IEEE Signal Process Mag 28(2):52–68
Wei S, Lin Z (2011) Analysis and improvement of low rank representation for subspace segmentation. arXiv preprint arXiv:1107.1561
Wei L, Wu A, Yin J (2015) Latent space robust subspace segmentation based on low-rank and locality constraints. Expert Syst Appl 42(19):6598–6608
Wei L, Wang X, Yin J, Wu A (2016) Spectral clustering steered low-rank representation for subspace segmentation. J Vis Commun Image Represent 38:386–395
Yin M, Gao J, Lin Z (2016) Laplacian regularized low-rank representation and its applications. IEEE Trans Pattern Anal Mach Intell 38(3):504–517
Yuan X, Yang J (2009) Sparse and low-rank matrix decomposition via alternating direction methods. Pac J Optim 9(1)
Zhang H, Lin Z, Zhang C, Gao J (2014) Robust latent low rank representation for subspace clustering. Neurocomputing 145:369–373
Zhang N, Yang J (2013) Low-rank representation based discriminative projection for robust feature extraction. Neurocomputing 111:13–20
Zhang Y, Jiang Z, Davis LS (2013) Learning structured low-rank representations for image classification. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 676–683
Zheng Z, Yu M, Jia J, Liu H, Xiang D, Huang X, Yang J (2014) Fisher discrimination based low rank matrix recovery for face recognition. Pattern Recogn 47(11):3502–3511
Zhou P, Lin Z, Zhang C (2016) Integrated low-rank-based discriminative feature learning for recognition. IEEE Trans Neural Netw Learn Syst 27(5):1080–1093
Acknowledgements
This work was partly supported by the National High Technology Research and Development Program (863Program) of China (2014AA015202) and the National Natural Science Foundation of China (61472030, 61572067, 61502024).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Communicated by V. Loia.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhao, X., An, G., Cen, Y. et al. Robust discriminant low-rank representation for subspace clustering. Soft Comput 23, 7005–7013 (2019). https://doi.org/10.1007/s00500-018-3339-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-018-3339-y