期刊
PROCEEDINGS OF THE IEEE
卷 106, 期 8, 页码 1411-1426出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/JPROC.2018.2846606
关键词
Convergence rate; convex optimization; iteration complexity; nonconvex optimization; principal component analysis (PCA); robust PCA (RPCA); c-stationary solution
资金
- National Science Foundation (NSF) [CMMI-1400217, CMMI-1635106]
- Army Research Office (ARO) [W911NF-17-1-0298]
Robust principal component analysis (RPCA) has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bioinformatics, statistics, and machine learning to image and video processing in computer vision. RPCA and its variants such as sparse PCA and stable PCA can be formulated as optimization problems with exploitable special structures. Many specialized efficient optimization methods have been proposed to solve robust PCA and related problems. In this paper, we review existing optimization methods for solving convex and nonconvex relaxations/variants of RPCA, discuss their advantages and disadvantages, and elaborate on their convergence behaviors. We also provide some insights for possible future research directions including new algorithmic frameworks that might be suitable for implementing on multiprocessor setting to handle large-scale problems.
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