Article

Robust subspace segmentation by low-rank representation

Authors:

Yong YuAuthors Info & Claims

ICML'10: Proceedings of the 27th International Conference on International Conference on Machine Learning

Pages 663 - 670

Published: 21 June 2010 Publication History

Abstract

We propose low-rank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowest-rank representation among all the candidates that represent all vectors as the linear combination of the bases in a dictionary. Unlike the well-known sparse representation (SR), which computes the sparsest representation of each data vector individually, LRR aims at finding the lowest-rank representation of a collection of vectors jointly. LRR better captures the global structure of data, giving a more effective tool for robust subspace segmentation from corrupted data. Both theoretical and experimental results show that LRR is a promising tool for subspace segmentation.

References

[1]

Cai, Jian-Feng, Candes, Emmanuel J., and Shen, Zuowei. A singular value thresholding algorithm for matrix completion. 2008.

[2]

Candes, Emmanuel J. and Plan, Yaniv. Matrix completion with noise. In IEEE Proceeding, 2009.

[3]

Candès, Emmanuel J. and Recht, Benjamin. Exact matrix completion via convex optimization. Foundations of Computational Mathematics, 2009.

Digital Library

[4]

Candès, Emmanuel J., Li, Xiaodong, Ma, Yi, and Wright, John. Robust principal component analysis?, 2009.

[5]

Costeira, Jo ao Paulo and Kanade, Takeo. A multi-body factorization method for independently moving objects. IJCV, pp. 159-179, 1998.

Digital Library

[6]

Eldar, Yonina C. and Mishali, Moshe. Robust recovery of signals from a union of subspaces. CoRR, 2008.

[7]

Elhamifar, Ehsan and Vidal, René. Sparse subspace clustering. In CVPR, pp. 2790-2797, 2009.

[8]

Fazel, M. Matrix rank minimization with applications. PhD thesis, 2002.

[9]

Fischler, Martin A. and Bolles, Robert C. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM, pp. 381-395, 1981.

Digital Library

[10]

Gruber, Amit and Weiss, Yair. Multibody factorization with uncertainty and missing data using the em algorithm. In CVPR, pp. 707-714, 2004.

[11]

Ho, Jeffrey, Yang, Ming-Hsuan, Lim, Jongwoo, Lee, Kuang-Chih, and Kriegman, David J. Clustering appearances of objects under varying illumination conditions. In CVPR, pp. 11-18, 2003.

Digital Library

[12]

Horn, R. and Johnson, C. Topics in Matrix Analysis. 1991.

Digital Library

[13]

Keshavan, Raghunandan, Montanari, Andrea, and Oh, Sewoong. Matrix completion from noisy entries. In NIPS, 2009.

Digital Library

[14]

Lee, K.C., Ho, J., and Kriegman, D. Acquiring linear subspaces for face recognition under variable lighting. TPAMI, pp. 684-698, 2005.

Digital Library

[15]

Lin, Zhouchen, Chen, Minming, Wu, Leqin, and Ma, Yi. The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. Technical report, UIUC Technical Report UILU-ENG-09-2215, 2009.

[16]

Lu, Le and Vidal, René. Combined central and sub-space clustering for computer vision applications. In ICML, pp. 593-600, 2006.

Digital Library

[17]

Ma, Yi, Derksen, H., Wei, Hong, and Wright, John. Segmentation of multivariate mixed data via lossy data coding and compression. CVIU, 2008a.

[18]

Ma, Yi, Yang, Allen, Derksen, Harm, and Fossum, Robert. Estimation of subspace arrangements with applications in modeling and segmenting mixed data. SIAM Review, pp. 413-458, 2008b.

Digital Library

[19]

Rao, Shankar, Tron, Roberto, Vidal, René, and Ma, Yi. Motion segmentation in the presence of outlying, incomplete, or corrupted trajectories. TPAMI, 2009.

Digital Library

[20]

Rao, Shankar, Yang, Allen, Sastry, Shankar, and Ma, Yi. Robust algebraic segmentation of mixed rigid-body and planar motions in two views. IJCV, pp. 425-446, 2010.

Digital Library

[21]

Shi, Jianbo and Malik, Jitendra. Normalized cuts and image segmentation. TPAMI, pp. 888-905, 2000.

Digital Library

[22]

Tron, Roberto and Vidal, René. A benchmark for the comparison of 3-d motion segmentation algorithms. In CVPR, 2007.

[23]

Wright, John, Tao, Yangyu, Lin, Zhouchen, Ma, Yi, and Shum, Heung-Yeung. Classification via minimum incremental coding length (MICL). In NIPS. 2008a.

Digital Library

[24]

Wright, John, Yang, Allen, Ganesh, A., Sastry, S. S., and Ma, Yi. Robust face recognition via sparse representation. TPAMI, pp. 210-227, 2008b.

Digital Library

[25]

Yan, Jingyu and Pollefeys, Marc. A general framework for motion segmentation: Independent, articulated, rigid, non-rigid, degenerate and non-degenerate. In ECCV, pp. 94-106, 2006.

Digital Library

[26]

Yang, Allen, Rao, Shankar, and Ma, Yi. Robust statistical estimation and segmentation of multiple sub-spaces. In CVPR Workshop, 2006.

Digital Library

[27]

Zhang, Teng, Szlam, Arthur, and Lerman, Gilad. Median k-flats for hybrid linear modeling with many outliers. CoRR, 2009.

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cover image Guide Proceedings

ICML'10: Proceedings of the 27th International Conference on International Conference on Machine Learning

June 2010

1262 pages

ISBN:9781605589077

Sponsors

NSF: National Science Foundation
Xerox
Microsoft Research: Microsoft Research
Yahoo!
IBM: IBM

Publisher

Omnipress

Madison, WI, United States

Publication History

Published: 21 June 2010

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Cited By

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https://dl.acm.org/doi/10.5555/3692070.3692728
Wang ZLiu ZHu DJia TLarson K(2024)Nonconvex multiview subspace clustering framework with efficient method designs and theoretical analysisProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/571(5162-5170)Online publication date: 3-Aug-2024
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Li XDai YWang BLi CGuan RGu FOuyang JLarson K(2024)WPML3CPProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/495(4479-4487)Online publication date: 3-Aug-2024
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Fei KPeng CKang KShao W(2022)Robust Sparse and Low-rank Subspace Clustering with Log-based Nonconvex ApproximationsProceedings of the 5th International Conference on Big Data Technologies10.1145/3565291.3565318(165-170)Online publication date: 23-Sep-2022
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