IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i1p187-197.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437109007547
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2009.09.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gustafsson, Mika & Hörnquist, Michael & Lombardi, Anna, 2006. "Comparison and validation of community structures in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 559-576.
    2. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    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. Zhang, Shihua & Wang, Rui-Sheng & Zhang, Xiang-Sun, 2007. "Identification of overlapping community structure in complex networks using fuzzy c-means clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 483-490.
    5. Medus, A. & Acuña, G. & Dorso, C.O., 2005. "Detection of community structures in networks via global optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 358(2), pages 593-604.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. You, Tao & Cheng, Hui-Min & Ning, Yi-Zi & Shia, Ben-Chang & Zhang, Zhong-Yuan, 2016. "Community detection in complex networks using density-based clustering algorithm and manifold learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 221-230.
    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.
    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. 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.
    5. Guo, Wei-Feng & Zhang, Shao-Wu, 2016. "A general method of community detection by identifying community centers with affinity propagation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 508-519.
    6. Chen, Zigang & Li, Lixiang & Peng, Haipeng & Liu, Yuhong & Yang, Yixian, 2018. "Attributed community mining using joint general non-negative matrix factorization with graph Laplacian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 324-335.
    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.
    8. Shen, Yi, 2014. "The similarity of weights on edges and discovering of community structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 560-570.
    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).
    12. Cheng, Hui-Min & Li, Si-Yan & Ning, Yi-Zi & Chen, Xing & Pan, Rui & Zhang, Zhong-Yuan, 2020. "Analysis on utilization of Beijing local roads using taxi GPS data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abdolhosseini-Qomi, Amir Mahdi & Yazdani, Naser & Asadpour, Masoud, 2020. "Overlapping communities and the prediction of missing links in multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    2. Zhang, Zhiwei & Wang, Zhenyu, 2015. "Mining overlapping and hierarchical communities in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 25-33.
    3. Wu, Jianshe & Wang, Xiaohua & Jiao, Licheng, 2012. "Synchronization on overlapping community network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 508-514.
    4. Badie, Reza & Aleahmad, Abolfazl & Asadpour, Masoud & Rahgozar, Maseud, 2013. "An efficient agent-based algorithm for overlapping community detection using nodes’ closeness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5231-5247.
    5. Chen, Duanbing & Shang, Mingsheng & Lv, Zehua & Fu, Yan, 2010. "Detecting overlapping communities of weighted networks via a local algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(19), pages 4177-4187.
    6. Nicolò Pecora & Pablo Rovira Kaltwasser & Alessandro Spelta, 2016. "Discovering SIFIs in Interbank Communities," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-17, December.
    7. Lan Huang & Guishen Wang & Yan Wang & Enrico Blanzieri & Chao Su, 2013. "Link Clustering with Extended Link Similarity and EQ Evaluation Division," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-18, June.
    8. Zhang, Hongli & Gao, Yang & Zhang, Yue, 2018. "Overlapping communities from dense disjoint and high total degree clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 286-298.
    9. Wu, Jianshe & Lu, Rui & Jiao, Licheng & Liu, Fang & Yu, Xin & Wang, Da & Sun, Bo, 2013. "Phase transition model for community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1287-1301.
    10. 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.
    11. Zhou, Xu & Liu, Yanheng & Zhang, Jindong & Liu, Tuming & Zhang, Di, 2015. "An ant colony based algorithm for overlapping community detection in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 289-301.
    12. Supreet Mandala & Soundar Kumara & Kalyan Chatterjee, 2014. "A Game-Theoretic Approach to Graph Clustering," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 629-643, August.
    13. 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.
    14. Mu, Caihong & Liu, Yong & Liu, Yi & Wu, Jianshe & Jiao, Licheng, 2014. "Two-stage algorithm using influence coefficient for detecting the hierarchical, non-overlapping and overlapping community structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 47-61.
    15. Gao, Yang & Zhang, Hongli & Zhang, Yue, 2019. "Overlapping community detection based on conductance optimization in large-scale networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 69-79.
    16. Zhenping Li & Xiang-Sun Zhang & Rui-Sheng Wang & Hongwei Liu & Shihua Zhang, 2013. "Discovering Link Communities in Complex Networks by an Integer Programming Model and a Genetic Algorithm," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-10, December.
    17. You, Tao & Cheng, Hui-Min & Ning, Yi-Zi & Shia, Ben-Chang & Zhang, Zhong-Yuan, 2016. "Community detection in complex networks using density-based clustering algorithm and manifold learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 221-230.
    18. Benati, Stefano & Puerto, Justo & Rodríguez-Chía, Antonio M. & Temprano, Francisco, 2022. "A mathematical programming approach to overlapping community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    19. Gao, Yang & Zhang, Hongli & Zhang, Yue, 2019. "Overlapping communities from lines and triangles in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 455-466.
    20. Xiaofeng Wang & Gongshen Liu & Jianhua Li & Jan P Nees, 2017. "Locating Structural Centers: A Density-Based Clustering Method for Community Detection," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-23, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:389:y:2010:i:1:p:187-197. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.