Accepted Paper: Rank minimization on tensor ring: An efficient approach for tensor decomposition and completion

Back to list of accepted papers


Longhao Yuan (Saitama Institute of Technology/RIKEN AIP); Chao Li (RIKEN); jianting cao (Saitama Institute of Technology); Qibin Zhao (RIKEN AIP)


In recent studies, tensor ring decomposition (TRD) has become a promising model for tensor completion. However, TRD is always suffering from the rank selection problem due to the undetermined multilinear rank. For tensor decomposition with missing entries, the sub-optimal rank selection of traditional methods always leads to the overfitting/underfitting problem. In this paper, we first explore the latent space of the TRD and theoretically prove the relationship between TR-rank and the rank of the tensor unfoldings. Then, we propose two tensor completion models by imposing the different low-rank regularizations on the TR-factors, by which the TRD is able to obtain the optimal TR-rank and explore more low-rank structures of the tensor. By employing the alternating direction method of multipliers (ADMM) scheme, our algorithms obtain the TR factors and the underlying tensor simultaneously. In experiments of tensor completion tasks, our algorithms show robustness to rank selection and high computation efficiency, in comparison to traditional low-rank approximation algorithms.