Provable Convex Co-clustering of Tensors

Eric C. Chi, Brian R. Gaines, Will Wei Sun, Hua Zhou, Jian Yang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
StatePublished - Oct 2020
Externally publishedYes


  • Clustering
  • Fused lasso
  • High-dimensional Statistical Learning
  • Multiway Data
  • Non-asymptotic Error

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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