Dynamic Tensor Clustering

TL;DR

This paper introduces a novel dynamic tensor clustering method that incorporates sparsity and fusion structures, providing strong statistical guarantees and computational efficiency, applicable to general-order tensor data.

Contribution

It proposes a new structured tensor factorization with an efficient optimization algorithm, offering theoretical error bounds and high-probability recovery of true clusters.

Findings

Method achieves accurate clustering in simulations.

Successfully applied to brain connectivity data.

Provides theoretical guarantees on estimator convergence.

Abstract

Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap between statistical guarantee and computational efficiency for existing tensor clustering solutions. In this article, we aim to bridge this gap by proposing a new dynamic tensor clustering method, which takes into account both sparsity and fusion structures, and enjoys strong statistical guarantees as well as high computational efficiency. Our proposal is based upon a new structured tensor factorization that encourages both sparsity and smoothness in parameters along the specified tensor modes. Computationally, we develop a highly efficient optimization algorithm that benefits from substantial dimension reduction. In theory, we first establish a non-asymptotic error bound for the estimator from the structured tensor factorization. Built upon this error bound, we then derive the rate of convergence of the estimated cluster centers, and show that the estimated clusters recover the true cluster structures with a high probability. Moreover, our proposed method can be naturally extended to co-clustering of multiple modes of the tensor data. The efficacy of our approach is illustrated via simulations and a brain dynamic functional connectivity analysis from an Autism spectrum disorder study.