---
title: "Nonconvex Relaxation Approaches to Robust Matrix Recovery"
authors:
  - "Shusen Wang"
  - "Dehua Liu"
  - "Zhihua Zhang"
doi: ""
url: "https://ijcai.org/proceedings/2013/261"
pdf: "https://ijcai.org/proceedings/2013/0261.pdf"
venue: "Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence"
year: 2013
pages: "1764-1769"
track: ""
keywords:
---

# Nonconvex Relaxation Approaches to Robust Matrix Recovery

Shusen Wang, Dehua Liu, Zhihua Zhang

*Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence*, pages 1764-1769.

## Abstract

Motivated by the recent developments of nonconvex penalties in sparsity modeling, we propose a nonconvex optimization model for handing the low-rank matrix recovery problem. Different from the famous robust principal component analysis (RPCA), we suggest recovering low-rank and sparse matrices via a nonconvex loss function and a nonconvex penalty. The advantage of the nonconvex approach lies in its stronger robustness. To solve the model, we devise a majorization-minimization augmented Lagrange multiplier (MM-ALM) algorithm which finds the local optimal solutions of the proposed nonconvex model. We also provide an efficient strategy to speedup MM-ALM, which makes the running time comparable with the state-of-the-art algorithm of solving RPCA. Finally, empirical results demonstrate the superiority of our nonconvex approach over RPCA in terms of matrix recovery accuracy.