Matrix completion via modified schatten 2/3-norm

Abstract

Low-rank matrix completion is a hot topic in the field of machine learning. It is widely used in image processing, recommendation systems and subspace clustering. However, the traditional method uses the nuclear norm to approximate the rank function, which leads to only the suboptimal solution. Inspired by the closed-form formulation of $$L_{2/3}$$ L 2 / 3 regularization, we propose a new truncated schatten 2/3-norm to approximate the rank function. Our proposed regularizer takes full account of the prior rank information and achieves a more accurate approximation of the rank function. Based on this regularizer, we propose a new low-rank matrix completion model. Meanwhile, a fast and efficient algorithm are designed to solve the proposed model. In addition, a rigorous mathematical analysis of the convergence of the proposed algorithm is provided. Finally, the superiority of our proposed model and method is investigated on synthetic data and recommender system datasets. All results show that our proposed algorithm is able to achieve comparable recovery performance while being faster and more efficient than state-of-the-art methods.