Grassmann averages for scalable robust PCA

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

Volumn , Issue , 2014, Pages 3810-3817

  Hauberg, Søren ^a   Feragen, Aasa ^a,b   Black, Michael J ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

computer vision; directional statistics; Grassmann manifold; machine learning; PCA; Robust PCA; subspace estimation

Indexed keywords

DIMENSIONALITY REDUCTION; GENETIC ALGORITHMS; LARGE DATASET; LEARNING SYSTEMS; SCALABILITY; STATISTICS; VECTORS;

DIRECTIONAL STATISTICS; GRASSMANN MANIFOLD; LOW COMPUTATIONAL COMPLEXITY; MEMORY REQUIREMENTS; ROBUST PCA; STATE-OF-THE-ART APPROACH; SUBSPACE ESTIMATION; VIDEO RESTORATION;

COMPUTER VISION;

EID: 84911387568     PISSN: 10636919     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2014.481     Document Type: Conference Paper

References (31)

1. R. Arora, A. Cotter, K. Livescu, and N. Srebro. Stochastic optimization for PCA and PLS. Communication, Control, and Computing (Allerton), pp. 861-868, 2012.
2. R. Basri and D. Jacobs. Lambertian reflectance and linear subspaces. TPAMI, 25(2):218-233, 2003.
3. M. J. Black and A. D. Jepson. EigenTracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation. IJCV, 26:63-84, 1998.
4. C. M. Bishop. Pattern Recognition and Machine Learning. Springer, 2006.
5. M. R. Bridson and A. Haefliger. Metric Spaces of NonPositive Curvature. Springer, 1999.
6. N. Campbell. Robust procedures in multivariate analysis I: Robust covariance estimation. Journal of the Royal Statistical Society. Series C (Applied Statistics), 29(3):231-237, 1980.
7. E. J. Candes, X. Li, Y. Ma, and J. Wright. Robust principal component analysis? ACM, 58(1):1-37, 2011.
8. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms. MIT Press, 3rd edition, 2009.
9. F. De la Torre and M. J. Black. A framework for robust subspace learning. IJCV, 54:117-142, 2003.
10. 1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization. ICML, pp. 281-288, 2006.
11. J. Feng, H. Xu, and S. Yan. Robust PCA in high-dimension: A deterministic approach. ICML, pp. 249-256, 2012.
12. S. Geman and D. McClure. Statistical methods for tomo-graphic image reconstruction. Bulletin of the International Statistical Institute, 52(4):5-21, 1987.
13. A. Georghiades, P. Belhumeur, and D. Kriegman. From few to many: Illumination cone models for face recognition under variable lighting and pose. TPAMI, 23(6):643-660, 2001.
14. G. H. Golub and C. F. Van Loan. Matrix Computations. The Johns Hopkins University Press, 3rd edition, Oct. 1996.
15. S. Hauberg, A. Feragen, M.J. Black. Supplementary Material. http://ps.is.tue.mpg.de/project/Robust-PCA
16. P. J. Huber. Robust Statistics. Wiley: New York, 1981.
17. P. J. Huber. Projection pursuit. Annals of Statistics, 13(2):435-475, 1985.
18. H. Ji, S. Huang, Z. Shen and Y. H. Xu. Robust video restoration by joint sparse and low rank matrix approximation. SI-IMS, 4(4):1122-1142, 2011.
19. I. Jolliffe. Principal Component Analysis. Springer, 2002.
20. N. Kwak. Principal Component Analysis Based on L1-Norm Maximization. TPAMI, 30(9):1672-1680, 2008.
21. J. Lee. Introduction to Smooth Manifolds. Springer, 2002.
22. F. C. Leone, L. S. Nelson, and R. B. Nottingham. The folded normal distribution. Technometrics, 3(4):543-550, 1961.
23. L. Li, W. Huang, I. Gu, and Q. Tian. Statistical modeling of complex backgrounds for foreground object detection. IEEE Trans. Image Process., 13(11):1459-1472, 2004.
24. 1Filtering. http://arxiv.org/abs/1108.5359, 2011
25. L.W. Mackey, A.S. Talwalkar and M.I. Jordan. Divide-and-Conquer Matrix Factorization. NIPS, pp. 1134-1142, 2011.
26. K. V. Mardia and P. E. Jupp. Directional Statistics. 1999.
27. Y. Mu, J. Dong, X. Yuan and S. Yan. Accelerated low-rank visual recovery by random projection. CVPR, pp. 2609-2616, 2011.
28. S. T. Roweis. EM algorithms for PCA and SPCA. NIPS. pp. 626-323, 1998.
29. R. Tron and R. Vidal. Distributed computer vision algorithms through distributed averaging. CVPR, pp. 57-63, 2011.
30. L. Xu and A. L. Yuille. Robust principal component analysis by self-organizing rules based on statistical physics approach. IEEE Trans. Neural Networks, 6(1):131-143, 1995.
31. L. W. Z. Lin, M. Chen and Y. Ma. The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. Technical report, UILU-ENG-09-2215, 2009.