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Community Detection in Multilayer Networks Based on Matrix Factorization and Spectral Embedding Method

Author

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  • Fengqin Tang

    (School of Mathematics Sciences, Huaibei Normal University, Huaibei 235000, China)

  • Xuejing Zhao

    (School of Mathematics and Statistics, Lanzhou University, Lanzhou 730033, China)

  • Cuixia Li

    (School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, China)

Abstract

Community detection remains a challenging research hotspot in network analysis. With the complexity of the network data structures increasing, multilayer networks, in which entities interact through multiple types of connections, prove to be effective in describing complex networks. The layers in a multilayer network may not share a common community structure. In this paper, we propose a joint method based on matrix factorization and spectral embedding to recover the groups not only for the layers but also for nodes. Specifically, the layers are grouped via the matrix factorization method with layer similarity-based regularization in the perspective of a mixture multilayer stochastic block model, and then the node communities within a layer group are revealed by clustering a combination of the spectral embedding derived from the adjacency matrices and the shared approximation matrix. Numerical studies show that the proposed method achieves competitive clustering results as the number of nodes and/or number of layers vary, together with different topologies of network layers. Additionally, we apply the proposed method on two real-world multilayer networks and obtain interesting findings which again highlight the effectiveness of our method.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1573-:d:1105829
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    References listed on IDEAS

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    1. Rossi, Luca & Magnani, Matteo, 2015. "Towards effective visual analytics on multiplex and multilayer networks," Chaos, Solitons & Fractals, Elsevier, vol. 72(C), pages 68-76.
    2. Jing Lei & Kehui Chen & Brian Lynch, 2020. "Consistent community detection in multi-layer network data," Biometrika, Biometrika Trust, vol. 107(1), pages 61-73.
    3. Lu, Hong & Sang, Xiaoshuang & Zhao, Qinghua & Lu, Jianfeng, 2020. "Community detection algorithm based on nonnegative matrix factorization and pairwise constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Fengqin Tang & Chunning Wang & Jinxia Su & Yuanyuan Wang, 2020. "Spectral clustering-based community detection using graph distance and node attributes," Computational Statistics, Springer, vol. 35(1), pages 69-94, March.
    5. Ma, Xiaoke & Gao, Lin & Yong, Xuerong & Fu, Lidong, 2010. "Semi-supervised clustering algorithm for community structure detection in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 187-197.
    6. N. Binkiewicz & J. T. Vogelstein & K. Rohe, 2017. "Covariate-assisted spectral clustering," Biometrika, Biometrika Trust, vol. 104(2), pages 361-377.
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