An Effective Tensor Completion Method Based on Multi-linear Tensor Ring Decomposition

By considering the balance unfolding scheme does help to catch the global information for tensor completion and the recently proposed tensor ring decomposition, in this paper a weighted multilinear tensor ring decomposition model is proposed for tensor completion and called MTRD. Utilizing the circular dimensional permutation invariance of tensor ring decomposition, a very balance matricization scheme $< k, d >$-unfolding is employed in MTRD. In order to evaluate MTRD, it is applied on both synthetic data and image tensor data, and the experiment results show that MTRD are able to achieve the desired relative square error by spending much less time than its compared methods, i.e. TMac-TT and TR-ALS. The results of image completion also show that MTRD outperforms its compared methods in relative square error. Specifically, TMac-TT and TR-ALS fails to get the same relative square error as MTRD and TR-ALS prevails TMac-TT but requiring a large amount of running time. To sum up, MTRD is more applicable than its compared methods.