Coupled Tensor Completion via Low-rank Tensor Ring

X, MONTH YEAR 1 Coupled Tensor Completion via Low-rank Tensor Ring Huyan Huang, Yipeng Liu, Senior Member, IEEE, Ce Zhu, Fellow, IEEE Abstract --The coupled tensor decomposition aims to reveal the latent data structure which may share common factors. Using the recently proposed tensor ring decomposition, in this paper we propose a non-convex method by alternately optimizing the latent factors. We provide an excess risk bound for the proposed alternating minimization model, which shows the improvement in completion performance. The proposed algorithm is validated on synthetic data. Index T erms--tensor ring, coupled tensor completion, alternating least squares, excess risk bound, permutational Rademacher complexity I. I NTRODUCTION Tensor is a multidimensional array and able to model the interaction between different modes in high-dimensional data.