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Semi-supervised spectral algorithms for community detection in complex networks based on equivalence of clustering methods

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  • Ma, Xiaoke
  • Wang, Bingbo
  • Yu, Liang

Abstract

Community detection is fundamental for revealing the structure-functionality relationship in complex networks, which involves two issues—the quantitative function for community as well as algorithms to discover communities. Despite significant research on either of them, few attempt has been made to establish the connection between the two issues. To attack this problem, a generalized quantification function is proposed for community in weighted networks, which provides a framework that unifies several well-known measures. Then, we prove that the trace optimization of the proposed measure is equivalent with the objective functions of algorithms such as nonnegative matrix factorization, kernel K-means as well as spectral clustering. It serves as the theoretical foundation for designing algorithms for community detection. On the second issue, a semi-supervised spectral clustering algorithm is developed by exploring the equivalence relation via combining the nonnegative matrix factorization and spectral clustering. Different from the traditional semi-supervised algorithms, the partial supervision is integrated into the objective of the spectral algorithm. Finally, through extensive experiments on both artificial and real world networks, we demonstrate that the proposed method improves the accuracy of the traditional spectral algorithms in community detection.

Suggested Citation

  • Ma, Xiaoke & Wang, Bingbo & Yu, Liang, 2018. "Semi-supervised spectral algorithms for community detection in complex networks based on equivalence of clustering methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 786-802.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:786-802
    DOI: 10.1016/j.physa.2017.08.116
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    References listed on IDEAS

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    1. 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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    3. 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.
    4. Aaron Clauset & Cristopher Moore & M. E. J. Newman, 2008. "Hierarchical structure and the prediction of missing links in networks," Nature, Nature, vol. 453(7191), pages 98-101, May.
    5. Ding, Chris & Li, Tao & Peng, Wei, 2008. "On the equivalence between Non-negative Matrix Factorization and Probabilistic Latent Semantic Indexing," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3913-3927, April.
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    Cited by:

    1. Ma, Xiaoke & Li, Dongyuan & Tan, Shiyin & Huang, Zhihao, 2019. "Detecting evolving communities in dynamic networks using graph regularized evolutionary nonnegative matrix factorization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 530(C), pages 1-1.
    2. Zhang, Zhong-Yuan & Gai, Yujie & Wang, Yu-Fei & Cheng, Hui-Min & Liu, Xin, 2018. "On equivalence of likelihood maximization of stochastic block model and constrained nonnegative matrix factorization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 687-697.
    3. Lin, Wei & Li, Min & Zhou, Shuming & Liu, Jiafei & Chen, Gaolin & Zhou, Qianru, 2021. "Phase transition in spectral clustering based on resistance matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    4. Wu, Qianyong & Hu, Jiang, 2024. "A spectral based goodness-of-fit test for stochastic block models," Statistics & Probability Letters, Elsevier, vol. 209(C).

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