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The Korean Institute of Commucations and Information Sciences (한국통신학회)
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빅데이터 분석을 위한 Rank-Sparsity 기반 신호처리기법

  • Published : 2014.10.31
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Abstract

주성분 분석 기법(PCA)는 가장 널리 사용되는 데이터 차원 감소 (dimensionality reduction) 기법으로 알려져 있다. 하지만 데이터에 이상점 (outlier)가 존재하는 환경에서는 성능이 크게 저하된다는 단점을 가지고 있다. Rank-Sparsity(Robust PCA) 기법은 주어진 행렬을 low-rank 행렬과 저밀도(sparse)행렬의 합으로 분해하는 방식으로, 이상점이 많은 환경에서 PCA기법을 효과적으로 대체할 수 있는 알고리즘으로 알려져 있다. 본 고에서는 RPCA 기법을 간략히 소개하고, 그의 적용분야, 및 알고리즘에 관한 연구들을 대해서 알아본다.

Keywords

References

  1. E. J. Candes, X. Li, Y. Ma, and J. Wright, "Robust Principal Component Analysis?," Journal of ACM 58(1), 1-37.
  2. V. Chandrasekaran, S. Sanghavi, P.A. Parrilo and A.S. Willsky, "Rank-Sparsity Incoherence for Matrix Decomposition," SIAM J. Optim., 21(2), 572-596, 2011. https://doi.org/10.1137/090761793
  3. L.Breiman, "Random Forests,"Technical report, Department of Statistics, University of California, 2001.
  4. J.E. Jackson. "A User's Guide to Principal Components," New York: John Wiley and Sons, 1991.
  5. I.T.Jolliffe, "Principal Component Analysis," Springer-Verlag, 1986.
  6. P. Huber, "Robust Statistics," Wiley and Sons, 1981
  7. R. Gnanadesikan and J. Kettenring, "Robust estimates, residuals, and outlier detection with multiresponse data," Biometrics, 28:81-124, 1972. https://doi.org/10.2307/2528963
  8. Q. Ke and T. Kanade, "Robust l1-norm factorization in the presence of outliers and missing data,"In Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition, 2005.
  9. M. Fischler and R. Bolles, "Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography," Communications of the ACM, 24:381-385, 1981. https://doi.org/10.1145/358669.358692
  10. F. De La Torre and M. Black, "A framework for robust subspace learning," International Journal on Computer Vision, 54:117-142, 2003. https://doi.org/10.1023/A:1023709501986
  11. H. Jiang, W. Deng, and Z. Shen, "Surveillance Video Processing Using Compressive Sensing," Inverse Problems and Imaging, Volume 6, No. 2, 201-214, 2012. https://doi.org/10.3934/ipi.2012.6.201
  12. Z. Zhang, A. Ganesh, X. Liang and Y. ma, "TILT: Transform Invariant Low-Rank Textures," International Journal of Computer Vision, 99(1), 1-24, 2012. https://doi.org/10.1007/s11263-012-0515-x
  13. A. Ganesh, K. Min, J. Wright and Y. Ma, "Principal Component Pursuit with reduced linear measurements,"Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on.
  14. E. J. Candes and B. Recht, "Exact Matrix Completion via Convex Optimization," Foundations of Computational Mathematics, 9(6), 717-772, 2009. https://doi.org/10.1007/s10208-009-9045-5
  15. E. J. Candes and Y. Plan, "Matrix Completion with Noise," Proceedings of IEEE, 98(6), 925-936, 2010. https://doi.org/10.1109/JPROC.2009.2035722
  16. R. H. Keshavan, A. Montanari and S. Oh, "Matrix Completion From a Few Entries," IEEE Transactions on Information Theory, 56(6), 2980-2998, 2010. https://doi.org/10.1109/TIT.2010.2046205
  17. M. Wootters, Y. Plan, M.A. Davenport and E. van den Berg, "Lower bounds for quantized matrix completion," Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on.
  18. A.Waters, A. Sankaranarayanan and R. Baraniuk, "SpaRCS: Recovering Low-Rank and Sparse Matrices from Compressive Measurements," Proceedings of the Neural Infromation Processing Systems (NIPS), 2011.
  19. M. Grant and S. Boyd, "CVX: Matlab software for disciplined convex programming." http://stanford. edu/-boyd/cvx, 2009
  20. J. Cai, E. J. Candes and Z. Shen, "A Singular Value Thresholding Algorithm for Matrix Completion, SIAM, J. Optim., 20(4), 1956-1982, 2010. https://doi.org/10.1137/080738970
  21. Z. Lin, A. Ganesh, J. Wright, L. Wu, M. Chen, and Y. Ma, "Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix," In Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2009.
  22. A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems,"SIAM Journal on Imaging Sciences, 2(1):183-202, Mar 2009. https://doi.org/10.1137/080716542
  23. X. Yuan and J. Yang, "Sparse and low-rank matrix decomposition via alternating direction method," Pacific J. Optim., vol.9, no.1, pp 167-180, 2013.
  24. 이형일, 이혁, 이정우, "부공간에의 사영에 기반한 RPCA 기법의 온라인 업데이트 기법", 한국통신학회 추계종합학술발표회, 2014