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Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants

Shiqian Ma(sqma***at***ucdavis.edu)
Necdet S. Aybat(nsa10***at***psu.edu)

Abstract: Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision. Robust PCA 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 robust PCA, 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 multi-processor setting to handle large-scale problems.

Keywords: PCA, Robust PCA, Convex Optimization, Nonconvex Optimization, Iteration Complexity, Convergence Rate, $\epsilon$-Stationary Solution

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Citation: to appear in Proceedings of the IEEE

Download: [PDF]

Entry Submitted: 06/09/2018
Entry Accepted: 06/09/2018
Entry Last Modified: 06/09/2018

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