IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v490y2018icp786-802.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117308440
    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.2017.08.116?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. 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.
    2. 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.
    3. 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.
    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.
    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. 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).

    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. 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.
    3. 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.
    4. Amulyashree Sridhar & Sharvani GS & AH Manjunatha Reddy & Biplab Bhattacharjee & Kalyan Nagaraj, 2019. "The Eminence of Co-Expressed Ties in Schizophrenia Network Communities," Data, MDPI, vol. 4(4), pages 1-23, November.
    5. 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).
    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. 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.
    8. 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.
    9. Liu, Ji & Deng, Guishi, 2009. "Link prediction in a user–object network based on time-weighted resource allocation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3643-3650.
    10. Weihua Zhan & Jihong Guan & Zhongzhi Zhang, 2017. "A New Method for Extracting the Hierarchical Organization of Networks," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1359-1385, September.
    11. Ding, Jin & Lu, Yong-Zai & Chu, Jian, 2013. "Studies on controllability of directed networks with extremal optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6603-6615.
    12. 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).
    13. Sun, Lijun & Axhausen, Kay W., 2016. "Understanding urban mobility patterns with a probabilistic tensor factorization framework," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 511-524.
    14. 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.
    15. 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.
    16. Nicolas Jouvin & Pierre Latouche & Charles Bouveyron & Guillaume Bataillon & Alain Livartowski, 2021. "Greedy clustering of count data through a mixture of multinomial PCA," Computational Statistics, Springer, vol. 36(1), pages 1-33, March.
    17. Akshat Singhal & Song Cao & Christopher Churas & Dexter Pratt & Santo Fortunato & Fan Zheng & Trey Ideker, 2020. "Multiscale community detection in Cytoscape," PLOS Computational Biology, Public Library of Science, vol. 16(10), pages 1-10, October.
    18. Bastian Schaefermeier & Gerd Stumme & Tom Hanika, 2021. "Topic space trajectories," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 5759-5795, July.
    19. 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.
    20. Travis R Meyer & Daniel Balagué & Miguel Camacho-Collados & Hao Li & Katie Khuu & P Jeffrey Brantingham & Andrea L Bertozzi, 2019. "A year in Madrid as described through the analysis of geotagged Twitter data," Environment and Planning B, , vol. 46(9), pages 1724-1740, November.

    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:490:y:2018:i:c:p:786-802. 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.