Bayesian Robust Tensor Ring Model for Incomplete Multiway Data
This work addresses robust tensor completion for multiway data analysis, offering an incremental improvement by automating rank selection to reduce bias in noisy conditions.
The paper tackled robust tensor completion with outlier corruption by proposing a Bayesian robust tensor ring decomposition method, which achieved significantly improved performance over state-of-the-art methods in experiments.
Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observation with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the existing methods either require a pre-assigned TR rank or aggressively pursue the minimum TR rank, thereby often leading to biased solutions in the presence of noise. In this paper, a Bayesian robust tensor ring decomposition (BRTR) method is proposed to give more accurate solutions to 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 slices of core tensor with marginal components, resulting in automatic TR rank detection. Extensive experiments show that BRTR can achieve significantly improved performance than other state-of-the-art methods.