Robust Schatten-p Norm Based Approach for Tensor Completion

Abstract

The matrix nuclear norm has been widely applied to approximate the matrix rank for low-rank tensor completion because of its convexity. However, this relaxation may make the solution seriously deviate from the original solution for real-world data recovery. In this paper, using a nonconvex approximation of rank, i.e., the Schatten-p norm, we propose a novel model for tensor completion. It’s hard to solve this model directly because the objective function of the model is nonconvex. To solve the model, we develop a variant of this model via the classical quadric penalty method, and propose an algorithm, i.e., SpBCD, based on the block coordinate descent method. Although the objective function of the variant is nonconvex, we show that the sequence generated by SpBCD is convergent to a critical point. Our numerical experiments on real-world data show that SpBCD delivers state-of-art performance in recovering missing data.