A cyclic weighted median method for L1 low-rank matrix factorization with missing entries

Proceedings of the 27th AAAI Conference on Artificial Intelligence, AAAI 2013

Volumn , Issue , 2013, Pages 704-710

  Meng, Deyu ^a   Xu, Zongben ^a   Zhang, Lei ^b   Zhao, Ji ^c  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^c CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COORDINATE DECENT ALGORITHMS; LOW-RANK MATRICES; LOW-RANK REPRESENTATIONS; NON-SMOOTHNESS; NONCONVEXITY; SUB-PROBLEMS; WEIGHTED MEDIAN; WEIGHTED MEDIAN FILTER;

ARTIFICIAL INTELLIGENCE;

PROBLEM SOLVING;

EID: 84893361849     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (41)

1. Aguiar, P.; Stosic, M.; and Xavier, J. 2008. Spectrally optimal factorization of incomplete matrices. In CVPR.
2. Basri, R., and Jacobs, D. 2003. Lambertian reflection and linear subspaces. IEEE Trans. PAMI 25:218-233.
3. Breheny, P., and Huang, J. 2011. Coordinate desent algorithms for nonconvex penalized regression, with applications to biological feature selection. Annals of Applied Statistics 5:232-253.
4. Brownrigg, D. R. K. 1984. The weighted median filter. Commun. Assoc. Comput. Mach. 27.
5. Buchanan, A. M., and Fitzgibbon, A.W. 2005. Damped newton algorithms for matrix factorization with missing data. In CVPR.
6. Candès, E. J., and Romberg, J. 2005. l1-MAGIC: recovery of sparse signals via convex programming. Technical Report, California Institute of Technology.
7. Candès, E.; Li, X.; Ma, Y.; and Wright, J. 2011. Robust principal component analysis? Journal of the ACM 58.
8. Cheng, C.; Yang, H.; King, I.; and Lyu, M. R. 2012a. Fused matrix factorization with geographical and social influence in location-based social networks. In AAAI.
9. Cheng, C.; Yang, H. Q.; King, I.; and Lyu, M. R. 2012b. Fused matrix factorization with geographical and social influence in location-based social networks. In AAAI.
10. De la Torre, F., and Black, M. J. 2003. A framework for robust subspace learning. IJCV 54:117-142.
11. Deerwester, S.; Dumais, S.; Furnas, G.; Landauer, T.; and Harshman, R. 1990. Indexing by latent semantic analysis. Journal of the American Society for Information Science 41.
12. Ding, C.; Zhou, D.; He, X.; and Zha, H. 2006. R1-PCA: Rotational invariant l1-norm principal component analysis for robust subspace factorization. In ICML.
13. Eriksson, A., and van den Hengel, A. 2010. Efficient computation of robust low-rank matrix approximations in the presence of missing data using the l1 norm. In CVPR.
14. Eriksson, A., and van den Hengel, A. 2012. Efficient computation of robust weighted low-rank matrix approximations using the l1 norm. IEEE Trans. PAMI 34:1681-1690.
15. Friedman, J.; Hastie, T.; and Höfling. 2007. Pathwise coordinate optimization. The Annals of Applied Statistics 1:302-332.
16. Friedman, J.; Hastie, T.; and Tibshirani, R. 2010. Regularized paths for generalized linear models via coordinate descent. Journal of Statistical Software 33:1-22.
17. Gabriel, K. R., and Zamir, S. 1979. Lower rank approximation of matrices by least squares with any choice of weights. Technometrics 21:489-498.
18. Georghiades, A.; Belhumeur, P.; and Kriegman, D. 2001. From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Trans. PAMI 23:643-660.
19. Gillis, N., and Glineur, F. 2011. Low-rank matrix approximation with weights or missing data is NP-hard. SIAM Journal of Matrix Analysis and Applications 32.
20. Golub, G., and Loan, C. V. 1989. Matrix Computation. Maryland: Johns Hopkins University Press.
21. Jacobs, D. 1997. Linear fitting with missing data: Applications to structure-from-motion and to characterizing intensity images. In CVPR.
22. Jeffreys, H., and Jeffreys, B. S. 1988. Methods of Mathematical Physics. Cambridge University Press.
23. Ji, H.; Liu, C.; Shen, Z.; and Xu, Y. 2010. Robust video denoising using low rank matrix completion. In CVPR.
24. Ke, Q., and Kanade, T. 2001. A subspace approach to layer extraction. In CVPR.
25. Ke, Q., and Kanade, T. 2005. Robust l1 norm factorization in the presence of outliers and missing data by alternative convex programming. In CVPR.
26. Koren, Y. 2008. Factorization meets the neighborhood: A multifaceted collaborative filtering model. In SIGKDD.
27. Kwak, N. 2008. Principal component analysis based on l1- norm maximization. IEEE Trans. PAMI 30:1672-1680.
28. Li, W. J., and Yeung, D. Y. 2009. Relation regularized matrix factorization. In IJCAI.
29. Lin, Z.; Chen, M.; and Ma, Y. 2009. The augmented lagrange multiplier method for exact recovery of corrupted low-Rank matrix. Technical Report UILU-ENG-09-2215.
30. Luo, D.; Ding, C.; and Huang, H. 2011. Cluster indicator decomposition for efficient matrix factorization. In IJCAI.
31. Okatani, T., and Deguchi, K. 2007. On the Wiberg algorithm for matrix factorization in the presence of missing components. IJCV 72:329-337.
32. Rauh, A., and Arce, G. R. 2010. A fast weighted median algorithm based on quickselect. In ICIP.
33. Shum, H.; Ikeuchi, K.; and Reddy, R. 1995. Principal component analysis with missing data and its application to polyhedral object modeling. IEEE Trans. PAMI 17:855-867.
34. Sinha, A. 2010. Topics in the analysis of sparse and irregularly spaced time dependent gene expression data. Columbia University, Doctoral Dissertation.
35. Srebro, N., and Jaakkola, T. 2003. Weighted low-rank approximations. In ICML.
36. Strelow, D. 2012. General and nested Wiberg minimization. In CVPR.
37. Sturm, P. 2000. Algorithms for plane-based pose estimation. In CVPR.
38. Tomasi, C., and Kanade, T. 1992. Shape and motion from image streams under orthography: A factorization method. IJCV 9:137-154.
39. Tseng, P. 2001. Convergence of a block coordinate descent method for nondifferentiable minimization. Journal of Optimization Theory and Applications 109:475-494.
40. Turk, M., and Pentland, A. 1991. Eigenfaces for recognition. Journal of Cognitive Neuroscience 3:71-86.
41. Wright, J.; Peng, Y.; Ma, Y.; Ganesh, A.; and Rao, S. 2009. Robust principal component analysis: Exact recovery of corrupted low-rank matrices by convex optimization. In NIPS.