NDLI: Constrained Cramér–Rao Bound on Robust Principal Component Analysis

Content Provider	IEEE Xplore Digital Library
Author	Gongguo Tang Nehorai, A.
Copyright Year	1991
Abstract	We investigate the behavior of the mean-square error (MSE) of low-rank and sparse matrix decomposition, in particular the special case of the robust principal component analysis (RPCA), and its generalization matrix completion and correction (MCC). We derive a constrained Cramér-Rao bound (CRB) for any locally unbiased estimator of the low-rank matrix and of the sparse matrix. We analyze the typical behavior of the constrained CRB for MCC where a subset of entries of the underlying matrix are randomly observed, some of which are grossly corrupted. We obtain approximated constrained CRBs by using a concentration of measure argument. We design an alternating minimization procedure to compute the maximum-likelihood estimator (MLE) for the low-rank matrix and the sparse matrix, assuming knowledge of the rank and the sparsity level. For relatively small rank and sparsity level, we demonstrate numerically that the performance of the MLE approaches the constrained CRB when the signal-to-noise-ratio is high. We discuss the implications of these bounds and compare them with the empirical performance of the accelerated proximal gradient algorithm as well as other existing bounds in the literature.
Sponsorship	IEEE Signal Processing Society
Starting Page	5070
Ending Page	5076
Page Count	7
File Size	1228030
File Format	PDF
ISSN	1053587X
Volume Number	59
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sparse matrices Principal component analysis Maximum likelihood estimation Robustness Matrix decomposition Signal to noise ratio Modeling robust principal component analysis Accelerated proximal gradient algorithm constrained Cramér–Rao bound matrix completion and correction maximum likelihood estimation mean-square error
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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