Robust Pca By Manifold Optimization

Keywords

Low-rank modeling; Manifold of low-rank matrices; Principal component analysis

Abstract

Robust PCA is a widely used statistical procedure to recover an underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank matrices and proposes two algorithms based on manifold optimization. It is shown that, with a properly designed initialization, the proposed algorithms are guaranteed to converge to the underlying low-rank matrix linearly. Compared with a previous work based on the factorization of low-rank matrices Yi et al. (2016), the proposed algorithms reduce the dependence on the condition number of the underlying low-rank matrix theoretically. Simulations and real data examples confirm the competitive performance of our method.

Publication Date

11-1-2018

Publication Title

Journal of Machine Learning Research

Volume

19

Document Type

Article

Personal Identifier

scopus

Socpus ID

85060528973 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85060528973

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