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An Algorithm Based on Non-Negative Matrix Factorization for Detecting Communities in Networks

Author

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  • Chenze Huang

    (Research and Development Institute, Northwestern Polytechnical University, Shenzhen 518057, China
    These authors contributed equally to this work.)

  • Ying Zhong

    (Research and Development Institute, Northwestern Polytechnical University, Shenzhen 518057, China
    These authors contributed equally to this work.)

Abstract

Community structure is a significant characteristic of complex networks, and community detection has valuable applications in network structure analysis. Non-negative matrix factorization (NMF) is a key set of algorithms used to solve the community detection issue. Nevertheless, the localization of feature vectors in the adjacency matrix, which represents the characteristics of complex network structures, frequently leads to the failure of NMF-based approaches when the data matrix has a low density. This paper presents a novel algorithm for detecting sparse network communities using non-negative matrix factorization (NMF). The algorithm utilizes local feature vectors to represent the original network topological features and learns regularization matrices. The resulting feature matrices effectively reveal the global structure of the data matrix, demonstrating enhanced feature expression capabilities. The regularized data matrix resolves the issue of localized feature vectors caused by sparsity or noise, in contrast to the adjacency matrix. The approach has superior accuracy in detecting community structures compared to standard NMF-based community detection algorithms, as evidenced by experimental findings on both simulated and real-world networks.

Suggested Citation

  • Chenze Huang & Ying Zhong, 2024. "An Algorithm Based on Non-Negative Matrix Factorization for Detecting Communities in Networks," Mathematics, MDPI, vol. 12(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:619-:d:1341722
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    References listed on IDEAS

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    1. Gergely Palla & Imre Derényi & Illés Farkas & Tamás Vicsek, 2005. "Uncovering the overlapping community structure of complex networks in nature and society," Nature, Nature, vol. 435(7043), pages 814-818, June.
    2. 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.
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