A Doubly-Enhanced EM Algorithm for Model-Based Tensor Clustering

TL;DR

This paper introduces a novel tensor clustering method using a tensor normal mixture model combined with a doubly-enhanced EM algorithm, achieving accurate clustering in high-dimensional tensor data.

Contribution

It develops a new probabilistic tensor clustering framework and a specialized EM algorithm tailored for tensor data, with theoretical guarantees and improved performance.

Findings

DEEM achieves consistent clustering in high dimensions.

The tensor normal mixture model effectively captures tensor correlations.

Numerical results show superior performance over existing methods.

Abstract

Modern scientific studies often collect data sets in the forms of tensors, which call for innovative statistical analysis methods. In particular, there is a pressing need for tensor clustering methods to understand the heterogeneity in the data. We propose a tensor normal mixture model (TNMM) approach to enable probabilistic interpretation and computational tractability. Our statistical model leverages the tensor covariance structure to reduce the number of parameters for parsimonious modeling, and at the same time explicitly exploits the correlations for better variable selection and clustering. We propose a doubly-enhanced expectation-maximization (DEEM) algorithm to perform clustering under this model. Both the E-step and the M-step are carefully tailored for tensor data in order to account for statistical accuracy and computational cost in high dimensions. Theoretical studies confirm that DEEM achieves consistent clustering even when the dimension of each mode of the tensors grows at an exponential rate of the sample size. Numerical studies demonstrate favorable performance of DEEM in comparison to existing methods.