Multiway clustering via tensor block models

TL;DR

This paper introduces a tensor block model for multiway clustering, providing a unified estimation method with theoretical guarantees and demonstrating superior performance on simulated and real data.

Contribution

The paper develops a novel tensor block model with a unified least-square estimation and theoretical accuracy guarantees for multiway clustering.

Findings

Establishes statistical convergence of the estimator.

Achieves partition consistency in clustering.

Demonstrates outperformance over previous methods in simulations and real data.

Abstract

We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a tensor block model, develop a unified least-square estimation, and obtain the theoretical accuracy guarantees for multiway clustering. The statistical convergence of the estimator is established, and we show that the associated clustering procedure achieves partition consistency. A sparse regularization is further developed for identifying important blocks with elevated means. The proposal handles a broad range of data types, including binary, continuous, and hybrid observations. Through simulation and application to two real datasets, we demonstrate the outperformance of our approach over previous methods.