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An alternating minimization method for robust principal component analysis
Shen, Yuan1; Xu, Hongyu1; Liu, Xin2,3
AbstractThis paper focuses on the solution of robust principal component analysis (RPCA) problems that arise in fields such as information theory, statistics, and engineering. We adopt a model that minimizes the sum of the observation error and sparsity measurement subject to the rank constraint. To solve this problem, we propose a two-step alternating minimization method. In the first step, a symmetric low-rank product minimization, which is essentially a partial singular value decomposition, is efficiently solved with moderate accuracy. The second step then derives a closed-form solution. The proposed approach is almost parameter-free, and global convergence to a strict local minimizer is guaranteed under very loose conditions. We compare the proposed approach with some existing solvers, and numerical experiments demonstrate the outstanding performance of our approach in solving synthetic and real RPCA test problems. In particular, we illustrate the significant potential of the proposed approach to solve large-size problems with moderate accuracy.
KeywordRobust principal component analysis symmetric low rank product minimization singular value decomposition alternating minimization
Funding ProjectNational Natural Science Foundation of China[11726618] ; National Natural Science Foundation of China[11401295] ; Major Program of the National Social Science Foundation of China[12ZD114] ; National Social Science Foundation of China[17BTQ063] ; National Social Science Foundation of China[15BGL158] ; Qinglan Project of Jiangsu Province ; NSFC[11622112] ; NSFC[11471325] ; NSFC[91530204] ; NSFC[11688101] ; National Center for Mathematics and Interdisciplinary Sciences, CAS ; Key Research Program of Frontier Sciences, CAS[QYZDJ-SSW-SYS010]
WOS Research AreaComputer Science ; Operations Research & Management Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000490007300007
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Document Type期刊论文
Corresponding AuthorShen, Yuan
Affiliation1.Nanjing Univ Finance & Econ, Sch Appl Math, Nanjing, Jiangsu, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China
3.Univ Chinese Acad Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Shen, Yuan,Xu, Hongyu,Liu, Xin. An alternating minimization method for robust principal component analysis[J]. OPTIMIZATION METHODS & SOFTWARE,2019,34(6):1251-1276.
APA Shen, Yuan,Xu, Hongyu,&Liu, Xin.(2019).An alternating minimization method for robust principal component analysis.OPTIMIZATION METHODS & SOFTWARE,34(6),1251-1276.
MLA Shen, Yuan,et al."An alternating minimization method for robust principal component analysis".OPTIMIZATION METHODS & SOFTWARE 34.6(2019):1251-1276.
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