Community detection on mixture multilayer networks via regularized tensor decomposition

Bing Yi Jing, Ting Li, Zhongyuan Lyu, Dong Xia

Research output: Journal article publicationJournal articleAcademic researchpeer-review

21 Citations (Scopus)


We study the problem of community detection in multilayer networks, where pairs of nodes can be related in multiple modalities. We introduce a general framework, that is, mixture multilayer stochastic block model (MMSBM), which includes many earlier models as special cases. We propose a tensor-based algorithm (TWIST) to reveal both global/local memberships of nodes, and memberships of layers. We show that the TWIST procedure can accurately detect the communities with small misclassification error as the number of nodes and/or number of layers increases. Numerical studies confirm our theoretical findings. To our best knowledge, this is the first systematic study on the mixture multilayer networks using tensor decomposition. The method is applied to two real datasets: worldwide trading networks and malaria parasite genes networks, yielding new and interesting findings.

Original languageEnglish
Pages (from-to)3181-3205
Number of pages25
JournalAnnals of Statistics
Issue number6
Publication statusPublished - Dec 2021


  • Multilayer network
  • Network community detection
  • Tensor
  • Tucker decomposition

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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