A closed form solution to robust subspace estimation and clustering

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

Volumn , Issue , 2011, Pages 1801-1807

  Favaro, Paolo ^a   Vidal, René ^b   Ravichandran, Avinash ^c  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b JOHNS HOPKINS UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINED OPTIMIZATION; PATTERN RECOGNITION; SHRINKAGE;

AFFINITY MATRIX; AUGMENTED LAGRANGIANS; CLOSED FORM SOLUTIONS; NONCONVEX PROBLEM; RANK MINIMIZATIONS; SINGULAR VALUES; SUBSPACE ESTIMATION; THRESHOLDING OPERATORS;

MATRIX ALGEBRA;

EID: 80052874540     PISSN: 10636919     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2011.5995365     Document Type: Conference Paper

References (23)

1. J.-F. Cai, E. J. Candes, and Z. Shen. A singular value thresholding algorithm for matrix completion. SIAM Journal of Optimization, 20(4):1956-1982, 2008.
2. E. Candes, X. Li, Y. Ma, and J. Wright. Robust principal component analysis. Journal of the ACM, (Submitted) 2010.
3. E. Candes and T. Tao. Decoding by linear programming. IEEE Transactions on Information Theory, 51(12):4203-4215, 2005.
4. V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky. Rank-Sparsity Incoherence for Matrix Decomposition. SIAM Journal on Optimization, 2009.
5. J. Costeira and T. Kanade. A multibody factorization method for independently moving objects. IJCV, 29(3):159-179, 1998.
6. 1 -norm solution is also the sparsest solution. Comm. on Pure and Applied Mathematics, 59(6):797-829, 2006.
7. E. Elhamifar and R. Vidal. Sparse subspace clustering. In IEEE CVPR, 2009.
8. E. Elhamifar and R. Vidal. Clustering disjoint subspaces via sparse representation. In IEEE ICASSP, 2010.
9. A. Gruber and Y. Weiss. Multibody factorization with uncertainty and missing data using the EM algorithm. In IEEE CVPR, 2004.
10. I. Jolliffe. Principal Component Analysis. Springer-Verlag, New York, 1986.
11. Z. Lin, M. Chen, L. Wu, and Y. Ma. The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. http://arxiv.org/abs/ 1009.5055, 2009.
12. G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma. Robust recovery of subspace structures by low-rank representation. In http://arxiv.org/pdf/1010. 2955v1, 2011.
13. G. Liu, Z. Lin, and Y. Yu. Robust subspace segmentation by low-rank representation. In ICML, 2010.
14. N. Ozay, M. Sznaier, C. Lagoa, and O. Camps. GPCA with denoising: A moments-based convex approach. In IEEE CVPR, 2010.
15. S. Rao, R. Tron, R. Vidal, and Y. Ma. Motion segmentation in the presence of outlying, incomplete, or corrupted trajectories. IEEE PAMI, 2009.
16. B. Recht, M. Fazel, and P. Parrilo. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Review, 52(3):471-501, 2010.
17. M. Tipping and C. Bishop. Mxtures of probabilistic principal component analyzers. Neural Computation, 11(2):443-482, 1999.
18. R. Tron and R. Vidal. A benchmark for the comparison of 3-D motion segmentation algorithms. In IEEE CVPR, 2007.
19. R. Vidal. Subspace clustering. Signal Processing Magazine, 28(2):52-68, 2011.
20. R. Vidal, Y. Ma, and S. Sastry. Generalized Principal Component Analysis (GPCA). IEEE PAMI, 27(12):1-15, 2005.
21. R. Vidal, R. Tron, and R. Hartley. Multiframe motion segmentation with missing data using PowerFactorization and GPCA. IJCV, 79(1):85-105, 2008.
22. U. von Luxburg. A tutorial on spectral clustering. Statistics and Computing, 17, 2007.
23. J. Yan and M. Pollefeys. A general framework for motion segmentation: Independent, articulated, rigid, non-rigid, degenerate and nondegenerate. In ECCV, 2006.