Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants

Shiqian Ma, Necdet S. Aybat

Research output: Contribution to journalReview article

2 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Article number8412568
Pages (from-to)1411-1426
Number of pages16
JournalProceedings of the IEEE
Volume106
Issue number8
DOIs
StatePublished - Aug 1 2018

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Principal component analysis
Bioinformatics
Computer vision
Learning systems
Statistics
Processing

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

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abstract = "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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Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants. / Ma, Shiqian; Aybat, Necdet S.

In: Proceedings of the IEEE, Vol. 106, No. 8, 8412568, 01.08.2018, p. 1411-1426.

Research output: Contribution to journalReview article

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