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Consistent community detection in multi-layer network data

Author

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  • Jing Lei
  • Kehui Chen
  • Brian Lynch

Abstract

SummaryWe consider multi-layer network data where the relationships between pairs of elements are reflected in multiple modalities, and may be described by multivariate or even high-dimensional vectors. Under the multi-layer stochastic block model framework we derive consistency results for a least squares estimation of memberships. Our theorems show that, as compared to single-layer community detection, a multi-layer network provides much richer information that allows for consistent community detection from a much sparser network, with required edge density reduced by a factor of the square root of the number of layers. Moreover, the multi-layer framework can detect cohesive community structure across layers, which might be hard to detect by any single-layer or simple aggregation. Simulations and a data example are provided to support the theoretical results.

Suggested Citation

  • Jing Lei & Kehui Chen & Brian Lynch, 2020. "Consistent community detection in multi-layer network data," Biometrika, Biometrika Trust, vol. 107(1), pages 61-73.
    • Handle: RePEc:oup:biomet:v:107:y:2020:i:1:p:61-73.
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    File URL: http://hdl.handle.net/10.1093/biomet/asz068
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    Citations

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    Cited by:

    1. Fengqin Tang & Xuejing Zhao & Cuixia Li, 2023. "Community Detection in Multilayer Networks Based on Matrix Factorization and Spectral Embedding Method," Mathematics, MDPI, vol. 11(7), pages 1-19, March.
    2. Su, Wenqing & Guo, Xiao & Chang, Xiangyu & Yang, Ying, 2024. "Spectral co-clustering in multi-layer directed networks," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).
    3. Li, Mengxue & von Sachs, Rainer & Pircalabelu, Eugen, 2024. "Time-varying degree-corrected stochastic block models," LIDAM Discussion Papers ISBA 2024014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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