Robust approximations of low-rank minimization for tensor completion

Abstract

Motivated by the nuclear norm of tensors and nonconvex approximations of matrix rank, we propose three robust approximations of multi-linear rank for tensor completion. For each method, we develop an efficient algorithm to solve the corresponding optimization problem. Besides, we prove that every cluster point of the sequence, generated by the respective algorithm, is a stationary point. To obtain a more robust reconstruction, we design an updating rule of parameters for each method. Our empirical experiments on real-world data show that the proposed methods deliver state-of-the-art performance in the reconstruction of low-rank tensors.