Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 439417, 10 pages
http://dx.doi.org/10.1155/2014/439417
Research Article

Low-Rank Representation for Incomplete Data

1School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China
2School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China

Received 20 August 2014; Revised 25 November 2014; Accepted 19 December 2014; Published 31 December 2014

Academic Editor: Wanquan Liu

Copyright © 2014 Jiarong Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Foundations of Computational Mathematics, vol. 9, no. 6, pp. 717–772, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. J. Wright, Y. Peng, Y. Ma, A. Ganesh, and S. Rao, “Robust principal component analysis: exact recovery of corrupted low-rank matrices by convex optimization,” in Proceedings of the 23rd Annual Conference on Neural Information Processing Systems (NIPS '09), vol. 22, pp. 2080–2088, December 2009. View at Scopus
  3. G. Liu, Z. Lin, and Y. Yu, “Robust subspace segmentation by low-rank representation,” in Proceedings of the 27th International Conference on Machine Learning, pp. 663–670, 2010.
  4. E. J. Candès, X. Li, Y. Ma, and J. Wright, “Robust principal component analysis?” Journal of the ACM, vol. 58, no. 3, article 11, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. T. Bouwmans and E. H. Zahzah, “Robust PCA via principal component pursuit: a review for a comparative evaluation in video surveillance,” Computer Vision and Image Understanding, vol. 122, pp. 22–34, 2014. View at Publisher · View at Google Scholar · View at Scopus
  6. J. D. M. Rennie and N. Srebro, “Fast maximum margin matrix factorization for collaborative prediction,” in Proceedings of the 22nd International Conference on Machine Learning (ICML '05), pp. 713–719, August 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. F. Nie, H. Wang, X. Cai et al., “Robust matrix completion via joint Schatten p-norm and lp-norm minimization,” in Proceedings of the 12th IEEE International Conference on Data Mining, pp. 566–574, 2012.
  8. G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust recovery of subspace structures by low-rank representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 1, pp. 171–184, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. R. Vidal and P. Favaro, “Low rank subspace clustering (LRSC),” Pattern Recognition Letters, vol. 43, no. 1, pp. 47–61, 2014. View at Publisher · View at Google Scholar · View at Scopus
  10. B. Recht, M. Fazel, and P. A. Parrilo, “Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization,” SIAM Review, vol. 52, no. 3, pp. 471–501, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. I. T. Jolliffe, Principal Component Analysis, Springer Series in Statistics, 2nd edition, 2002.
  12. F. De La Torre and M. J. Black, “Robust principal component analysis for computer vision,” in Proceedings of the 8th International Conference on Computer Vision, pp. 362–369, July 2001. View at Scopus
  13. C. Ding, D. Zhou, X. He et al., “R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization,” in Proceedings of the 23rd International Conference on Machine Learning, pp. 281–288, 2006.
  14. J.-F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM Journal on Optimization, vol. 20, no. 4, pp. 1956–1982, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Z. Zhou, X. Li, J. Wright, E. Candès, and Y. Ma, “Stable principal component pursuit,” in Proceedings of the IEEE International Symposium on Information Theory (ISIT '10), pp. 1518–1522, Austin, Tex, USA, June 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. Z. Lin, M. Chen, L. Wu et al., “The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices,” Tech. Rep. UILU-ENG-09-2215, UIUC, 2010. View at Google Scholar
  17. X. Yuan and J. Yang, “Sparse and low-rank matrix decomposition via alternating direction methods,” Technical Report of Hong Kong Baptist University, 2009. View at Google Scholar
  18. D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods, Computer Science and Applied Mathematics, Academic Press, New York, NY, USA, 1982. View at MathSciNet
  19. E. Elhamifar and R. Vidal, “Sparse subspace clustering: algorithm, theory, and applications,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 11, pp. 2765–2781, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. J. Shi, X. Zheng, and L. Yong, “Incomplete robust principal component analysis,” ICIC Express Letters Part B: Applications, vol. 5, no. 6, pp. 1531–1538, 2014. View at Google Scholar
  21. Y. Liu and F. Shang, “An efficient matrix factorization method for tensor completion,” IEEE Signal Processing Letters, vol. 20, no. 4, pp. 307–310, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 2, pp. 210–227, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. A. Ng, M. Jordan, and Y. Weiss, “On spectral clustering: analysis and an algorithm,” in Advances in Neural Information Processing Systems, vol. 14, pp. 849–856, 2002. View at Google Scholar
  24. A. S. Georghiades, P. N. Belhumeur, and D. J. Kriegman, “From few to many: illumination cone models for face recognition under variable lighting and pose,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 643–660, 2001. View at Publisher · View at Google Scholar · View at Scopus
  25. R. Vidal and R. Hartley, “Three-view multibody structure from motion,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 2, pp. 214–227, 2008. View at Publisher · View at Google Scholar · View at Scopus