Volume 38, Issue 2
Robust Inexact Alternating Optimization for Matrix Completion with Outliers

J. Comp. Math., 38 (2020), pp. 337-354.

Published online: 2020-02

[An open-access article; the PDF is free to any online user.]

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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.

• Keywords

Matrix completion, ADMM, Outlier noise, Inexact projection.

65K05, 90C06, 93C41

keelee@csrc.ac.cn (Ji Li)

jfcai@ust.hk (Jian-Feng Cai)

zhao@uci.edu (Hongkai Zhao)

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@Article{JCM-38-337, author = {Li , Ji and Cai , Jian-Feng and Zhao , Hongkai }, title = {Robust Inexact Alternating Optimization for Matrix Completion with Outliers}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {2}, pages = {337--354}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1809-m2018-0106}, url = {http://global-sci.org/intro/article_detail/jcm/14520.html} }
TY - JOUR T1 - Robust Inexact Alternating Optimization for Matrix Completion with Outliers AU - Li , Ji AU - Cai , Jian-Feng AU - Zhao , Hongkai JO - Journal of Computational Mathematics VL - 2 SP - 337 EP - 354 PY - 2020 DA - 2020/02 SN - 38 DO - http://doi.org/10.4208/jcm.1809-m2018-0106 UR - https://global-sci.org/intro/article_detail/jcm/14520.html KW - Matrix completion, ADMM, Outlier noise, Inexact projection. AB -

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.

Ji Li, Jian-Feng Cai & Hongkai Zhao. (2020). Robust Inexact Alternating Optimization for Matrix Completion with Outliers. Journal of Computational Mathematics. 38 (2). 337-354. doi:10.4208/jcm.1809-m2018-0106
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