Model-Based Tensor Low-Rank Clustering

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.

KEYWORDS:

• Dimension reduction
• EM algorithm
• Mixture models
• Sparsity
• Tucker decomposition

Acknowledgments

We are grateful to the editor, associate editor, and referees, whose suggestions led to the great improvement of our work. We thank Dr. Biao Cai, Dr. Jingfei Zhang, and Dr. Will Wei Sun for sharing their code for HECM.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

This work was supported by the National Science Foundation under grant CCF-1908969.