Bayesian Robust Tucker Decomposition for Multiway Data Analysis

Tensor decomposition is an effective tool for dealing with higher-order data. Recently, robust tensor decomposition has demonstrated its powerful ability to fit higher-order data and combat noise for multiway data analysis. In this paper, we propose a Bayesian Robust Tucker Decomposition (BRTD) method which can automatically determine an optimal multi-linear rank for Tucker model without tuning any parameters. Specifically, for the generative process, we specify a hierarchical sparsity-inducing prior for automatic rank determination. For Bayesian inference, we present a variational Bayesian framework for BRTD model learning. Experimental results on the simulated and real surveillance video datasets demonstrate its superiority over other state-of-the-art methods.