An alternating minimization method for robust principal component analysis

doi:10.1080/10556788.2018.1496086

	An alternating minimization method for robust principal component analysis
	Shen, Yuan 1; Xu, Hongyu 1; Liu, Xin2,3
	2019-11-02
发表期刊	OPTIMIZATION METHODS & SOFTWARE
ISSN	1055-6788
卷号	34 期号:6 页码:1251-1276
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.
关键词	Robust principal component analysis symmetric low rank product minimization singular value decomposition alternating minimization
DOI	10.1080/10556788.2018.1496086
语种	英语
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
WOS类目	Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000490007300007
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35850
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.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
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.