Provable Model for Tensor Ring Completion

Tensor completion aims to recover a multi-dimensional array from its incomplete observations. The recently proposed tensor ring (TR) decomposition has powerful representation ability and shows promising performance in tensor completion, though they suffer from lack of theoretical guarantee. In this paper, we rigorously analyze the sample complexity of TR completion and find it also possesses the balance characteristic, which is consistent with the result of matrix completion. Inspired by this property we propose a nuclear norm minimization model and solve it by the alternating direction method of multipliers (ADMM). The experiments on synthetic data verify the theoretic analysis, and the numerical results of real-world data demonstrate that the proposed method gains great performance improvement in tensor completion compared with the state-of-the-art ones.