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Robust principal component analysis

Robust Principal Component Analysis (RPCA) is a modification of the widely used statistical procedure of principal component analysis (PCA) which works well with respect to grossly corrupted observations. A number of different approaches exist for Robust PCA, including an idealized version of Robust PCA, which aims to recover a low-rank matrix L0 from highly corrupted measurements M = L0 +S0.[1] This decomposition in low-rank and sparse matrices can be achieved by techniques such as Principal Component Pursuit method (PCP),[1] Stable PCP,[2] Quantized PCP,[3] Block based PCP,[4] and Local PCP.[5] Then, optimization methods are used such as the Augmented Lagrange Multiplier Method (ALM[6]), Alternating Direction Method (ADM[7]), Fast Alternating Minimization (FAM[8]), Iteratively Reweighted Least Squares (IRLS [9][10][11]) or alternating projections (AP[12][13][14]).

  1. ^ a b Cite error: The named reference RPCA was invoked but never defined (see the help page).
  2. ^ J. Wright; Y. Peng; Y. Ma; A. Ganesh; S. Rao (2009). "Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices by Convex Optimization". Neural Information Processing Systems, NIPS 2009.
  3. ^ S. Becker; E. Candes, M. Grant (2011). "TFOCS: Flexible First-order Methods for Rank Minimization". Low-rank Matrix Optimization Symposium, SIAM Conference on Optimization.
  4. ^ G. Tang; A. Nehorai (2011). "Robust principal component analysis based on low-rank and block-sparse matrix decomposition". 2011 45th Annual Conference on Information Sciences and Systems. pp. 1–5. doi:10.1109/CISS.2011.5766144. ISBN 978-1-4244-9846-8. S2CID 17079459.
  5. ^ B. Wohlberg; R. Chartrand; J. Theiler (2012). "Local principal component pursuit for nonlinear datasets". 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). pp. 3925–3928. doi:10.1109/ICASSP.2012.6288776. ISBN 978-1-4673-0046-9. S2CID 2747520.
  6. ^ Z. Lin; M. Chen; L. Wu; Y. Ma (2013). "The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices". Journal of Structural Biology. 181 (2): 116–27. arXiv:1009.5055. doi:10.1016/j.jsb.2012.10.010. PMC 3565063. PMID 23110852.
  7. ^ X. Yuan; J. Yang (2009). "Sparse and Low-Rank Matrix Decomposition via Alternating Direction Methods". Optimization Online.
  8. ^ P. Rodríguez; B. Wohlberg (2013). "Fast principal component pursuit via alternating minimization". 2013 IEEE International Conference on Image Processing. pp. 69–73. doi:10.1109/ICIP.2013.6738015. ISBN 978-1-4799-2341-0. S2CID 5726914.
  9. ^ C. Guyon; T. Bouwmans; E. Zahzah (2012). "Foreground Detection via Robust Low Rank Matrix Decomposition including Spatio-Temporal Constraint". International Workshop on Background Model Challenges, ACCV 2012.
  10. ^ C. Guyon; T. Bouwmans; E. Zahzah (2012). "Foreground Detection via Robust Low Rank Matrix Factorization including Spatial Constraint with Iterative Reweighted Regression". International Conference on Pattern Recognition, ICPR 2012.
  11. ^ C. Guyon; T. Bouwmans; E. Zahzah (2012). "Moving Object Detection via Robust Low Rank Matrix Decomposition with IRLS scheme". International Symposium on Visual Computing, ISVC 2012.
  12. ^ Cite error: The named reference netrapalli2014non was invoked but never defined (see the help page).
  13. ^ Cite error: The named reference cai2019accelerated was invoked but never defined (see the help page).
  14. ^ Cite error: The named reference cai2021rapid was invoked but never defined (see the help page).

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