Model-Based Tensor Low-Rank Clustering

Abstract

ABSTRACT Tensors have become prevalent in business applications and scientific studies. It is of great interest to analyze and understand the heterogeneity in tensor-variate observations. We propose a novel tensor low-rank mixture model (TLMM) to conduct efficient estimation and clustering on tensors. The model combines the Tucker low-rank structure in mean contrasts and the separable covariance structure to achieve parsimonious and interpretable modeling. To implement efficient computation under this model, we develop a low-rank enhanced expectation-maximization (LEEM) algorithm. The pseudo E-step and the pseudo M-step are carefully designed to incorporate variable selection and efficient parameter estimation. Numerical results in extensive experiments demonstrate the encouraging performance of the proposed method compared to popular vector and tensor methods. Supplementary materials for this article are available online.