Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from laborious model selection problem due to high model sensitivity. Especially for tensor ring (TR) decomposition, the number of model possibility grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure on TR latent space, we propose a novel tensor completion method, which is robust to model selection. In contrast to imposing low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in that the optimization step using singular value decomposition (SVD) can be performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm effectively alleviates the burden of TR-rank selection, therefore the computational cost is greatly reduced. The extensive experimental results on synthetic data and real-world data demonstrate the superior high performance and efficiency of the proposed approach against the state-of-the-art algorithms.