Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants
This is an incremental review paper that synthesizes and analyzes optimization techniques for robust PCA and its variants, which are important for applications in bio-informatics, statistics, machine learning, and computer vision.
The paper reviews existing optimization methods for solving convex and nonconvex relaxations and variants of robust PCA, discussing their advantages, disadvantages, and convergence behaviors, while also suggesting future research directions like new algorithmic frameworks for multi-processor settings to handle large-scale problems.
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.