A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers

Tao, Ting; Xiao, Lianghai; Zhong, Jiayuan

doi:10.3390/math13091466

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Open AccessArticle

A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers

by

Ting Tao

¹,

Lianghai Xiao

^2,* and

Jiayuan Zhong

^1,*

¹

School of Mathematics, Foshan University, Foshan 528011, China

²

College of Information Science and Technology, Jinan University, Guangzhou 510632, China

^*

Authors to whom correspondence should be addressed.

Mathematics 2025, 13(9), 1466; https://doi.org/10.3390/math13091466

Submission received: 20 March 2025 / Revised: 21 April 2025 / Accepted: 26 April 2025 / Published: 29 April 2025

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Abstract

This paper concerns a class of robust factorization models of low-rank matrix recovery, which have been widely applied in various fields such as machine learning and imaging sciences. An

ℓ_{1}

-loss robust factorized model incorporating the

ℓ_{2, 0}

-norm regularization term is proposed to address the presence of outliers. Since the resulting problem is nonconvex, nonsmooth, and discontinuous, an approximation problem that shares the same set of stationary points as the original formulation is constructed. Subsequently, a proximal alternating minimization method is proposed to solve the approximation problem. The global convergence of its iterate sequence is also established. Numerical experiments on matrix completion with outliers and image restoration tasks demonstrate that the proposed algorithm achieves low relative errors in shorter computational time, especially for large-scale datasets.

Keywords: matrix recovery with outliers; global convergence; column ℓ2,0-norm; alternating method

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MDPI and ACS Style

Tao, T.; Xiao, L.; Zhong, J. A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers. Mathematics 2025, 13, 1466. https://doi.org/10.3390/math13091466

AMA Style

Tao T, Xiao L, Zhong J. A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers. Mathematics. 2025; 13(9):1466. https://doi.org/10.3390/math13091466

Chicago/Turabian Style

Tao, Ting, Lianghai Xiao, and Jiayuan Zhong. 2025. "A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers" Mathematics 13, no. 9: 1466. https://doi.org/10.3390/math13091466

APA Style

Tao, T., Xiao, L., & Zhong, J. (2025). A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers. Mathematics, 13(9), 1466. https://doi.org/10.3390/math13091466

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A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers

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