A Nonconvex Projection Method for Robust PCA

Dutta, Aritra; Hanzely, Filip; Richtarik, Peter

A Nonconvex Projection Method for Robust PCA

Files

1805.07962v1.pdf (4.89 MB)

Type

Article

Authors

Dutta, Aritra
Hanzely, Filip

Richtarik, Peter

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Computer Science Program

Date

2019-09-13

Abstract

Robust principal component analysis (RPCA) is a well-studied problem whose goal is to decompose a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and apply an alternating projection method to solve it. To the best of our knowledge, this is the first paper proposing a method that solves RPCA problem without considering any objective function, convex relaxation, or surrogate convex constraints. We demonstrate through extensive numerical experiments on a variety of applications, including shadow removal, background estimation, face detection, and galaxy evolution, that our approach matches and often significantly outperforms current state-of-the-art in various ways.

Citation

Dutta, A., Hanzely, F., & Richtàrik, P. (2019). A Nonconvex Projection Method for Robust PCA. Proceedings of the AAAI Conference on Artificial Intelligence, 33, 1468–1476. doi:10.1609/aaai.v33i01.33011468