Home Page

Papers

Submissions

News

Editorial Board

Proceedings

Open Source Software

Search

Statistics

Login

Frequently Asked Questions

Contact Us



RSS Feed

Provable Convex Co-clustering of Tensors

Eric C. Chi, Brian J. Gaines, Will Wei Sun, Hua Zhou, Jian Yang; 21(214):1−58, 2020.

Abstract

Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently in modern scientific and business applications. Moreover, there is a gap between statistical guarantees and computational efficiency for existing tensor clustering solutions due to the nature of their non-convex formulations. In this work, we bridge this gap by developing a provable convex formulation of tensor co-clustering. Our convex co-clustering (CoCo) estimator enjoys stability guarantees and its computational and storage costs are polynomial in the size of the data. We further establish a non-asymptotic error bound for the CoCo estimator, which reveals a surprising “blessing of dimensionality” phenomenon that does not exist in vector or matrix-variate cluster analysis. Our theoretical findings are supported by extensive simulated studies. Finally, we apply the CoCo estimator to the cluster analysis of advertisement click tensor data from a major online company. Our clustering results provide meaningful business insights to improve advertising effectiveness.

[abs][pdf][bib]       
© JMLR 2020. (edit, beta)