Rank/norm regularization with closed-form solutions: Application to subspace clustering

Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011

Volumn , Issue , 2011, Pages 778-785

  Yu, Yao Liang ^a   Schuurmans, Dale ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE;

CLOSED FORM SOLUTIONS; GENERAL CLASS; SUB-SPACE CLUSTERING; UNITARILY INVARIANT NORM;

CLUSTERING ALGORITHMS;

EID: 80053161077     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. Cai, J.-F., Candies, E. J., and Shen, Z. (2010). A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 20(4):1956-1982.
2. Costeira, J. P. and Kanade, T. (1998). A multibody factorization method for independently moving objects. International Journal of Computer Vision, 29(3):159-179. (Pubitemid 128517909)
3. Eckart, C. and Young, G. (1936). The approximation of one matrix by another of lower rank. Psychometrika, 1(3):211-218.
4. Elhamifar, E. and Vidal, R. (2009). Sparse subspace clustering. In IEEE conference on Computer Vision and Pattern Recognition, pages 2790-2797.
5. Friedland, S. and Torokhti, A. (2007). Generalized rankconstrained matrix approximations. SIAM Journal on Matrix Analysis and Applications, 29(2):656-659.
6. Jollier, I. T. (2002). Principal Component Analysis. Springer, 2nd edition.
7. Liu, G., Lin, Z., Yan, S., Yu, Y., and Ma, Y. (2010a). Robust recovery of subspace structures by low-rank representation. http://arxiv.org/pdf/1010. 2955v3.
8. Liu, G., Lin, Z., and Yu, Y. (2010b). Robust subspace segmentation by low-rank representation. In International Conference on Machine Learning, pages 663-670.
9. Luxburg, U. (2007). A tutorial on spectral clustering. Statistics and Computing, 17:395-416.
10. Ma, S., Goldfarb, D., and Chen, L. (2011). Fixed point and bregman iterative methods for matrix rank minimization. Mathematical Programming, 128:321-353.
11. Ma, Y., Derksen, H., Hong, W., and Wright, J. (2007). Segmentation of multivariate mixed data via lossy data coding and compression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29:1546-1562. (Pubitemid 47299910)
12. Marshall, A. W., Olkin, I., and Arnold, B. C. (2011). Inequalities: Theory of Majorization and Its Applications. Springer, 2nd edition.
13. Mirsky, L. (1960). Symmetric gauge functions and unitarily invariant norms. Quarterly Journal of Mathematics, 11(2):50-59.
14. Ni, Y. Z., Sun, J., Yuan, X., Yan, S., and Cheong, L.-F. (2010). Robust low-rank subspace segmentation with semide finite guarantees. In ICDM Workshop on Optimization Based Methods for Emerging Data Mining Problems.
15. Penrose, R. (1956). On best approximate solutions of linear matrix equations. Mathematical Proceedings of the Cambridge Philosophical Society, 52(01):17-19.
16. Piotrowski, T., Cavalcante, R. L. G., and Yamada, I. (2009). Stochastic mv-pure estimatorrobust reducedrank estimator for stochastic linear model. IEEE Transactions on Signal Processing, 57(4):1293-1303.
17. Piotrowski, T. and Yamada, I. (2008). Mv-pure estimator minimum-variance pseudo-unbiased reduced-rank estimator for linearly constrained ill-conditioned inverse problems. IEEE Transactions on Signal Processing, 56(8):3408-3423.
18. Seung, H. S. and Lee, D. D. (2000). The manifold ways of perception. Science, 290:2268-2269. (Pubitemid 32041555)
19. Sondermann, D. (1986). Best approximate solutions to matrix equations under rank restrictions. Statistical Papers, 27:57-66.
20. Tian, Y. (2003). Ranks of solutions of the matrix equation AXB = C. Linear and Multilinear Algebra, 51(2):111-125. (Pubitemid 36594337)
21. Tron, R. and Vidal, R. (2007). A benchmark for the comparison of 3-d motion segmentation algorithms. In IEEE conference on Computer Vision and Pattern Recognition, pages 1-8.
22. Vidal, R. (2011). Subspace clustering. IEEE Signal Processing Magazine, 28(2):52-68.
23. Vidal, R., Ma, Y., and Sastry, S. (2005). Generalized principal component analysis (gpca). IEEE Transactions on Pattern Analysis and Machine Intelligence, 27:1945-1959. (Pubitemid 43051391)
24. Zelnik-Manor, L. and Irani, M. (2006). On single-sequence and multi-sequence factorizations. International Journal of Computer Vision, 67(3):313-326. (Pubitemid 43741486)