Dynamic Tensor Clustering

Will Wei Sun, Lexin Li

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. There is also a gap between statistical guarantee and computational efficiency for existing tensor clustering solutions. In this article, we propose a new dynamic tensor clustering method that works for a general-order dynamic tensor, and enjoys both strong statistical guarantee and high computational efficiency. Our proposal is based on a new structured tensor factorization that encourages both sparsity and smoothness in parameters along the specified tensor modes. Computationally, we develop a highly efficient optimization algorithm that benefits from substantial dimension reduction. Theoretically, we first establish a nonasymptotic error bound for the estimator from the structured tensor factorization. Built upon this error bound, we then derive the rate of convergence of the estimated cluster centers, and show that the estimated clusters recover the true cluster structures with high probability. Moreover, our proposed method can be naturally extended to co-clustering of multiple modes of the tensor data. The efficacy of our method is illustrated through simulations and a brain dynamic functional connectivity analysis from an autism spectrum disorder study. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1894-1907
Number of pages14
JournalJournal of the American Statistical Association
Issue number528
StatePublished - Oct 2 2019


  • Cluster analysis
  • Multidimensional array
  • Nonconvex optimization
  • Tensor decomposition
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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