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Published in: Soft Computing 16/2019

21-06-2018 | Methodologies and Application

Robust discriminant low-rank representation for subspace clustering

Authors: Xian Zhao, Gaoyun An, Yigang Cen, Hengyou Wang, Ruizhen Zhao

Published in: Soft Computing | Issue 16/2019

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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.

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Literature
go back to reference Chen J, Yi Z (2014) Sparse representation for face recognition by discriminative low-rank matrix recovery. J Vis Commun Image Represent 25(5):763–773CrossRef Chen J, Yi Z (2014) Sparse representation for face recognition by discriminative low-rank matrix recovery. J Vis Commun Image Represent 25(5):763–773CrossRef
go back to reference 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 (2009) Sparse subspace clustering. In: IEEE conference on computer vision and pattern recognition, 2009, CVPR 2009, pp 2790–2797
go back to reference Elhamifar E, Vidal R (2013) Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781CrossRef Elhamifar E, Vidal R (2013) Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781CrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference 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 (2011) Latent low-rank representation for subspace segmentation and feature extraction. In: 2011 IEEE international conference on computer vision (ICCV), pp 1615–1622
go back to reference 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, Yan S (2014) Latent low-rank representation. In: Fu Y (ed) Low-rank and sparse modeling for visual analysis. Springer, Cham
go back to reference 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, 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
go back to reference 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):171–184CrossRef 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):171–184CrossRef
go back to reference 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):646–654MathSciNetCrossRefMATH 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):646–654MathSciNetCrossRefMATH
go back to reference Lvd Maaten, Hinton G (2008) Visualizing data using t-sne. J Mach Learn Res 9:2579–2605MATH Lvd Maaten, Hinton G (2008) Visualizing data using t-sne. J Mach Learn Res 9:2579–2605MATH
go back to reference Duda O, Hart P, Stork DG (2000) Pattern classification. Wiley, HobokenMATH Duda O, Hart P, Stork DG (2000) Pattern classification. Wiley, HobokenMATH
go back to reference Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905CrossRef Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905CrossRef
go back to reference Wei L, Wu A, Yin J (2015) Latent space robust subspace segmentation based on low-rank and locality constraints. Expert Syst Appl 42(19):6598–6608CrossRef Wei L, Wu A, Yin J (2015) Latent space robust subspace segmentation based on low-rank and locality constraints. Expert Syst Appl 42(19):6598–6608CrossRef
go back to reference Wei L, Wang X, Yin J, Wu A (2016) Spectral clustering steered low-rank representation for subspace segmentation. J Vis Commun Image Represent 38:386–395CrossRef Wei L, Wang X, Yin J, Wu A (2016) Spectral clustering steered low-rank representation for subspace segmentation. J Vis Commun Image Represent 38:386–395CrossRef
go back to reference Yin M, Gao J, Lin Z (2016) Laplacian regularized low-rank representation and its applications. IEEE Trans Pattern Anal Mach Intell 38(3):504–517CrossRef Yin M, Gao J, Lin Z (2016) Laplacian regularized low-rank representation and its applications. IEEE Trans Pattern Anal Mach Intell 38(3):504–517CrossRef
go back to reference Yuan X, Yang J (2009) Sparse and low-rank matrix decomposition via alternating direction methods. Pac J Optim 9(1) Yuan X, Yang J (2009) Sparse and low-rank matrix decomposition via alternating direction methods. Pac J Optim 9(1)
go back to reference Zhang H, Lin Z, Zhang C, Gao J (2014) Robust latent low rank representation for subspace clustering. Neurocomputing 145:369–373CrossRef Zhang H, Lin Z, Zhang C, Gao J (2014) Robust latent low rank representation for subspace clustering. Neurocomputing 145:369–373CrossRef
go back to reference Zhang N, Yang J (2013) Low-rank representation based discriminative projection for robust feature extraction. Neurocomputing 111:13–20CrossRef Zhang N, Yang J (2013) Low-rank representation based discriminative projection for robust feature extraction. Neurocomputing 111:13–20CrossRef
go back to reference 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 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
go back to reference 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):3502–3511CrossRef 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):3502–3511CrossRef
go back to reference Zhou P, Lin Z, Zhang C (2016) Integrated low-rank-based discriminative feature learning for recognition. IEEE Trans Neural Netw Learn Syst 27(5):1080–1093MathSciNetCrossRef Zhou P, Lin Z, Zhang C (2016) Integrated low-rank-based discriminative feature learning for recognition. IEEE Trans Neural Netw Learn Syst 27(5):1080–1093MathSciNetCrossRef
Metadata
Title
Robust discriminant low-rank representation for subspace clustering
Authors
Xian Zhao
Gaoyun An
Yigang Cen
Hengyou Wang
Ruizhen Zhao
Publication date
21-06-2018
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 16/2019
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-018-3339-y

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