Two-Step Proximal Gradient Algorithm for Low-Rank Matrix Completion

Qiuyu Wang, Wenjiao Cao, Zhengfen Jin

Abstract


In this paper, we  propose a two-step proximal gradient algorithm to solve nuclear norm regularized least squares for the purpose of recovering low-rank data matrix from sampling of its entries. Each iteration generated by the proposed algorithm is a combination of the latest three points, namely, the previous point, the current iterate, and its proximal gradient point. This algorithm preserves the computational simplicity of classical proximal gradient algorithm where a singular value decomposition in proximal operator is involved. Global convergence is followed directly in the literature. Numerical results are reported to show the efficiency of the algorithm.

Keywords


Matrix nuclear norm minimization, Matrix completion, Proximal gradient algorithm, Singular value decomposition

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DOI: 10.19139/soic.v4i2.201

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