Bayesian Robust Tensor Ring Model for Incomplete Multiway Data

TL;DR

This paper introduces a Bayesian robust tensor ring model that automatically determines tensor rank and improves recovery of incomplete, noisy multiway data, outperforming existing methods.

Contribution

It proposes a Bayesian approach for tensor ring decomposition that automatically detects tensor rank and handles outliers without pre-setting parameters.

Findings

BRTR achieves superior recovery accuracy compared to state-of-the-art methods.

The method automatically detects tensor rank during learning.

Extensive experiments validate the effectiveness of BRTR.

Abstract

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.