Dual Smoothing and Level Set Techniques for Variational Matrix Decomposition

TL;DR

This paper reviews convex formulations for robust PCA, introduces dual smoothing and level set techniques with new theoretical insights, and demonstrates their effectiveness through numerical experiments on simulated and real data.

Contribution

It presents novel theoretical results and applies dual smoothing and level set methods to improve convex optimization solutions for RPCA.

Findings

Enhanced convex formulations for RPCA

Improved optimization techniques with dual smoothing and level set methods

Successful numerical experiments on real-world data

Abstract

We focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants. We then review dual smoothing and level set techniques in convex optimization, present several novel theoretical results, and apply the techniques on the RPCA problem. In the final sections, we show a range of numerical experiments for simulated and real-world problems.