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Statistics > Methodology

Title: Provable Convex Co-clustering of Tensors

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 is both computationally and storage efficient. 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.
Subjects: Methodology (stat.ME); Applications (stat.AP); Computation (stat.CO); Machine Learning (stat.ML)
Cite as: arXiv:1803.06518 [stat.ME]
  (or arXiv:1803.06518v1 [stat.ME] for this version)

Submission history

From: Eric Chi [view email]
[v1] Sat, 17 Mar 2018 15:15:28 GMT (120kb,D)