Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants

TL;DR

This paper reviews optimization algorithms for robust PCA and its variants, analyzing their efficiencies, convergence, and potential for large-scale applications, aiming to guide future research directions.

Contribution

It provides a comprehensive review of existing optimization methods for robust PCA, highlighting their advantages, disadvantages, and convergence properties, and suggests new research directions.

Findings

Various optimization methods have different convergence behaviors.

Specialized algorithms improve efficiency for large-scale robust PCA.

Future frameworks may leverage multi-processor systems.

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.