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In tensor completion tasks, the traditional low-rank tensor decompositionmodels suffer from the laborious model selection problem due to their highmodel sensitivity. In particular, for tensor ring (TR) decomposition, thenumber of model possibilities grows exponentially with the tensor order, whichmakes it rather challenging to find the optimal TR decomposition. In thispaper, by exploiting the low-rank structure of the TR latent space, we proposea novel tensor completion method which is robust to model selection. Incontrast to imposing the low-rank constraint on the data space, we introducenuclear norm regularization on the latent TR factors, resulting in theoptimization step using singular value decomposition (SVD) being performed at amuch smaller scale. By leveraging the alternating direction method ofmultipliers (ADMM) scheme, the latent TR factors with optimal rank and therecovered tensor can be obtained simultaneously. Our proposed algorithm isshown to effectively alleviate the burden of TR-rank selection, thereby greatlyreducing the computational cost. The extensive experimental results on bothsynthetic and real-world data demonstrate the superior performance andefficiency of the proposed approach against the state-of-the-art algorithms.

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