DBLTD: Deep Bayesian Low-Rank Tensor Decomposition for Multivariate Data Analysis

Abstract

Low-rank tensor decomposition has attracted growing attention in multivariate data analysis owning to its potentials of capturing latent representations of multivariate data correlating various data attributes. However, existing studies still have limited capabilities to represent the nonlinear relationships within multivariate data. Moreover, their performance tends to degrade under the circumstance of intensive noise embedded in the source data as well as improper setting of initial tensor rank. To tackle the challenges, this study proposes a Deep Bayesian Low-rank Tensor Decomposition (DBLTD) framework to handle the multivariate data: 1) DBLTD first establishes a probabilistic tensor decomposition model and imposes a Gaussian-Gamma sparsity prior over factor matrices and noise tensor to induce the sparse components of multidomain factors and separate the noise from the source data, respectively, 2) A generative convolution network is designed on the basis of multiple convolution blocks to produce the distributions of deep factors along with deep parameters in a self-training manner, 3) The framework develops a deep variational Bayesian inference algorithm with guaranteed convergence for model training, where the loss function is constituted of reconstruction error and sparse constraint term over deep factors and parameters. Experimental results on diverse multivariate datasets indicate that DBLTD is effective to learn the tensor rank and reduce the impact of various noises during multivariate data decomposition. Furthermore, DBLTD has demonstrated remarkable advantages in decomposition-based medical applications like blind EEG denoising, structural EEG feature construction and MRI image restoration.