Bayesian adaptive tensor ring decomposition with automatic model selection.

Robust tensor decomposition (RTD) is designed to distinguish low-rank and sparse tensors from noisy high-dimensional data, which holds fundamental significance in the fields of machine learning and computer vision. Nevertheless, current RTD-based methods fall short in addressing the issues of automatic noise adaptation and determination of model capacity. In response to these challenges, this paper introduces a robust non-parametric Bayesian method known as the Bayesian adaptive tensor ring decomposition (BATR) method. More precisely, BATR models unknown noise using a Dirichlet process Gaussian mixture model (DP-GMM), with automatic determination of the noise components. Besides, BATR accomplishes an adaptive low tensor ring (TR) rank model by incorporating a more advanced generalized hyperbolic (GH) prior into the probabilistic framework, thereby facilitating automatic TR rank determination. Furthermore, a variational Bayesian inference algorithm is employed to update the posteriors of the model. Extensive experiments on synthetic data, color images, face images, multispectral images, and hyperspectral images demonstrate the improved performance of BATR compared to other state-of-the-art methods.