Spectral Clustering via Adaptive Layer Aggregation for Multi-Layer Networks

Sihan Huang, Haolei Weng, Yang Feng

Research output: Contribution to journalArticlepeer-review


One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches based on effective convex layer aggregations. Our aggregation methods are strongly motivated by a delicate asymptotic analysis of the spectral embedding of weighted adjacency matrices and the downstream k-means clustering, in a challenging regime where community detection consistency is impossible. In fact, the methods are shown to estimate the optimal convex aggregation, which minimizes the misclustering error under some specialized multi-layer network models. Our analysis further suggests that clustering using Gaussian mixture models is generally superior to the commonly used k-means in spectral clustering. Extensive numerical studies demonstrate that our adaptive aggregation techniques, together with Gaussian mixture model clustering, make the new spectral clustering remarkably competitive compared to several popularly used methods. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1170-1184
Number of pages15
JournalJournal of Computational and Graphical Statistics
Issue number3
StatePublished - 2023


  • Asymptotic misclustering error
  • Community detection
  • Convex aggregation
  • Eigenvalue ratio
  • Gaussian mixture distributions
  • Multi-layer networks
  • Spectral clustering
  • k-means

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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