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An alternating minimization method for robust principal component analysis

文献类型：期刊论文

作者Shen, Yuan3; Xu, Hongyu3; Liu, Xin1,2
刊名OPTIMIZATION METHODS & SOFTWARE
出版日期2019-11-02
卷号34期号:6页码:1251-1276
关键词Robust principal component analysis symmetric low rank product minimization singular value decomposition alternating minimization
ISSN号1055-6788
DOI10.1080/10556788.2018.1496086
英文摘要This 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.
资助项目National 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研究方向Computer Science ; Operations Research & Management Science ; Mathematics
语种英语
WOS记录号WOS:000490007300007
出版者TAYLOR & FRANCIS LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/35849]  
专题计算数学与科学工程计算研究所
通讯作者Shen, Yuan
作者单位1.Univ Chinese Acad Sci, Beijing, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China
3.Nanjing Univ Finance & Econ, Sch Appl Math, Nanjing, Jiangsu, Peoples R China
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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