Low Rank Matrix Minimization with a Truncated Difference of Nuclear Norm and Frobenius Norm Regularization

Abstract

In this paper, we present a novel regularization with a truncated difference of nuclear norm and Frobenius norm of form $L_{t,*-\alpha F}$ with an integer $t$ and parameter $\alpha$ for rank minimization problem. The forward-backward splitting (FBS) algorithm is proposed to solve such a regularization problem, whose subproblems are shown to have closed-form solutions. We show that any accumulation point of the sequence generated by the FBS algorithm is a first-order stationary point. In the end, the numerical results demonstrate that the proposed FBS algorithm outperforms the existing methods.

Quan Yu

PhD student

My research interests include low rank tensor optimization, image processing and machine learning.