ROBUST INEXACT ALTERNATING OPTIMIZATION FOR MATRIX COMPLETION WITH OUTLIERS |
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Authors: | Ji Li Jian-Feng Cai & Hongkai Zhao |
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Institution: | Beijing Computational Science Research Center, Beijing 100193, China;Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay,Kowloon, Hong Kong;Department of Mathematics, University of California, Irvine, CA, USA |
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Abstract: | We investigate the problem of robust matrix completion with a fraction of observation corrupted by sparsity outlier noise. We propose an algorithmic framework based on the ADMM algorithm for a non-convex optimization, whose objective function consists of an $\ell_1$ norm data fidelity and a rank constraint. To reduce the computational cost per iteration, two inexact schemes are developed to replace the most time-consuming step in the generic ADMM algorithm. The resulting algorithms remarkably outperform the existing solvers for robust matrix completion with outlier noise. When the noise is severe and the underlying matrix is ill-conditioned, the proposed algorithms are faster and give more accurate solutions than state-of-the-art robust matrix completion approaches. |
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Keywords: | Matrix completion ADMM Outlier noise Inexact projection |
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