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Tieniu Tan , Institute of Automation, Chinese Academy of Sciences, Beijing
Ran He , Institute of Automation, Chinese Academy of Sciences, Beijing
ABSTRACT
Low-rank matrix recovery algorithms aim to recover a corrupted low-rank matrix with sparse errors. However, corrupted errors may not be sparse in real-world problems and the relationship between L1 regularizer on noise and robust M-estimators is still unknown. This paper proposes a general robust framework for low-rank matrix recovery via implicit regularizers of robust M-estimators, which are derived from convex conjugacy and can be used to model arbitrarily corrupted errors. Based on the additive form of half-quadratic optimization, proximity operators of implicit regularizers are developed such that both low-rank structure and corrupted errors can be alternately recovered. In particular, the dual relationship between the absolute function in L1 regularizer and Huber M-estimator is studied, which establishes a relationship between robust low-rank matrix recovery methods and M-estimators based robust principal component analysis methods. Extensive experiments on synthetic and real-world datasets corroborate our claims and verify the robustness of the proposed framework.
INDEX TERMS
Robustness, Principal component analysis, Optimization, Sparse matrices, Equations, Minimization, Kernel, regularizer, robust principal component analysis, low-rank matrix recovery, correntropy
CITATION
Tieniu Tan, Ran He, "Robust Recovery of Corrupted Low-rank Matrix by Implicit Regularizers", IEEE Transactions on Pattern Analysis & Machine Intelligence, , no. 1, pp. 1, PrePrints PrePrints, doi:10.1109/TPAMI.2013.188
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