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Nonconvex Relaxation Approaches to Robust Matrix Recovery

Shusen Wang, Dehua Liu, Zhihua Zhang

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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.

Shusen Wang, Dehua Liu, and Zhihua Zhang. 2013. Nonconvex Relaxation Approaches to Robust Matrix Recovery. In Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, IJCAI-13. IJCAI, 1764–1769. https://ijcai.org/proceedings/2013/261
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