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On equivalence of likelihood maximization of stochastic block model and constrained nonnegative matrix factorization

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  • Zhang, Zhong-Yuan
  • Gai, Yujie
  • Wang, Yu-Fei
  • Cheng, Hui-Min
  • Liu, Xin

Abstract

Community structures detection in complex network is important for understanding not only the topological structures of the network, but also the functions of it. Stochastic block model and nonnegative matrix factorization are two widely used methods for community detection, which are proposed from different perspectives. In this paper, the relations between them are studied. The logarithm of likelihood function for stochastic block model can be reformulated under the framework of nonnegative matrix factorization. Despite model equivalence, the algorithms employed by the two methods are different. Preliminary numerical experiments are carried out to compare the behaviors of the algorithms, demonstrating that the multiplicative update rules for NMF are more effective.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:503:y:2018:i:c:p:687-697
    DOI: 10.1016/j.physa.2018.02.068
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    References listed on IDEAS

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    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. Zhong-Yuan Zhang & Yong-Yeol Ahn, 2015. "Community detection in bipartite networks using weighted symmetric binary matrix factorization," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(09), pages 1-14.
    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. 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.
    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. Cai, Chunhao & Cheng, Xuwen & Xiao, Weilin & Wu, Xiang, 2019. "Parameter identification for mixed fractional Brownian motions with the drift parameter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).

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