Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization

TL;DR

This paper introduces a novel tensor clustering method using heterogeneous Tucker decomposition and manifold optimization, avoiding vectorization to better exploit multiarray data structures.

Contribution

It proposes a new subspace clustering algorithm based on heterogeneous Tucker decomposition and manifold optimization, with closed-form updates and a trust-region algorithm for the last mode.

Findings

Effective clustering performance comparable to state-of-the-art methods

Utilizes second-order Riemannian geometry for optimization

Avoids vectorization, preserving tensor structure

Abstract

Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing multiarray data has been extensively researched. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model. In contrast to existing techniques, we propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the so-called multinomial manifold, for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.