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Semi-supervised clustering algorithm for community structure detection in complex networks

Author

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  • Ma, Xiaoke
  • Gao, Lin
  • Yong, Xuerong
  • Fu, Lidong

Abstract

Discovering a community structure is fundamental for uncovering the links between structure and function in complex networks. In this paper, we discuss an equivalence of the objective functions of the symmetric nonnegative matrix factorization (SNMF) and the maximum optimization of modularity density. Based on this equivalence, we develop a new algorithm, named the so-called SNMF-SS, by combining SNMF and a semi-supervised clustering approach. Previous NMF-based algorithms often suffer from the restriction of measuring network topology from only one perspective, but our algorithm uses a semi-supervised mechanism to get rid of the restriction. The algorithm is illustrated and compared with spectral clustering and NMF by using artificial examples and other classic real world networks. Experimental results show the significance of the proposed approach, particularly, in the cases when community structure is obscure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:1:p:187-197
    DOI: 10.1016/j.physa.2009.09.018
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    References listed on IDEAS

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    2. 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.
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    4. Da Kuang & Sangwoon Yun & Haesun Park, 2015. "SymNMF: nonnegative low-rank approximation of a similarity matrix for graph clustering," Journal of Global Optimization, Springer, vol. 62(3), pages 545-574, July.
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    7. Eustace, Justine & Wang, Xingyuan & Cui, Yaozu, 2015. "Overlapping community detection using neighborhood ratio matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 510-521.
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    9. 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.
    10. 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.
    11. Ning, Yi-Zi & Liu, Xin & Cheng, Hui-Min & Zhang, Zhong-Yuan, 2020. "Effects of social network structures and behavioral responses on the spread of infectious diseases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
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    13. 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.
    14. Li, Yafang & Jia, Caiyan & Yu, Jian, 2015. "A parameter-free community detection method based on centrality and dispersion of nodes in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 321-334.
    15. Nan, Dong-Yang & Yu, Wei & Liu, Xiao & Zhang, Yun-Peng & Dai, Wei-Di, 2018. "A framework of community detection based on individual labels in attribute networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 523-536.
    16. Chen, Chunchun & Zhu, Wenjie & Peng, Bo, 2022. "Differentiated graph regularized non-negative matrix factorization for semi-supervised community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    17. Li, Yafang & Jia, Caiyan & Li, Jianqiang & Wang, Xiaoyang & Yu, Jian, 2018. "Enhanced semi-supervised community detection with active node and link selection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 219-232.
    18. 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.
    19. Liu, Dong & Liu, Xiao & Wang, Wenjun & Bai, Hongyu, 2014. "Semi-supervised community detection based on discrete potential theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 173-182.
    20. Liang Yang & Meng Ge & Di Jin & Dongxiao He & Huazhu Fu & Jing Wang & Xiaochun Cao, 2017. "Exploring the roles of cannot-link constraint in community detection via Multi-variance Mixed Gaussian Generative Model," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-21, July.

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