A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers
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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">...
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MDPI AG
2025-04-01
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| author | Ting Tao Lianghai Xiao Jiayuan Zhong |
| author_facet | Ting Tao Lianghai Xiao Jiayuan Zhong |
| author_sort | Ting Tao |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mn>1</mn></msub></semantics></math></inline-formula>-loss robust factorized model incorporating the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mrow><mn>2</mn><mo>,</mo><mn>0</mn></mrow></msub></semantics></math></inline-formula>-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. |
| format | Article |
| id | doaj-art-88e9ea177bb74a32ac1c53b1986a88e2 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
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| series | Mathematics |
| spelling | doaj-art-88e9ea177bb74a32ac1c53b1986a88e22025-08-20T02:58:44ZengMDPI AGMathematics2227-73902025-04-01139146610.3390/math13091466A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with OutliersTing Tao0Lianghai Xiao1Jiayuan Zhong2School of Mathematics, Foshan University, Foshan 528011, ChinaCollege of Information Science and Technology, Jinan University, Guangzhou 510632, ChinaSchool of Mathematics, Foshan University, Foshan 528011, ChinaThis 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mn>1</mn></msub></semantics></math></inline-formula>-loss robust factorized model incorporating the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mrow><mn>2</mn><mo>,</mo><mn>0</mn></mrow></msub></semantics></math></inline-formula>-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.https://www.mdpi.com/2227-7390/13/9/1466matrix recovery with outliersglobal convergencecolumn ℓ2,0-normalternating method |
| spellingShingle | Ting Tao Lianghai Xiao Jiayuan Zhong A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers Mathematics matrix recovery with outliers global convergence column ℓ2,0-norm alternating method |
| title | A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers |
| title_full | A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers |
| title_fullStr | A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers |
| title_full_unstemmed | A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers |
| title_short | A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers |
| title_sort | fast proximal alternating method for robust matrix factorization of matrix recovery with outliers |
| topic | matrix recovery with outliers global convergence column ℓ2,0-norm alternating method |
| url | https://www.mdpi.com/2227-7390/13/9/1466 |
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