Bayesian Robust Tensor Ring Decomposition for Incomplete Multiway Data

Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observations with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the methods using the TR model either require a preassigned TR rank or aggressively pursue the minimum TR rank, where the latter often leads to biased solutions in the presence of noise. To tackle these bottlenecks, a Bayesian robust TR decomposition (BRTR) method is proposed to give a more accurate solution for the RTC problem, which can avoid exquisite selection of the TR rank and penalty parameters. A variational Bayesian (VB) algorithm is developed to infer the probability distribution of posteriors. During the learning process, BRTR can prune off zero components of core tensors, resulting in automatic TR rank determination. Extensive experiments show that BRTR can achieve significantly improved performance than other state-of-the-art methods.