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A Deep Stochastic Model for Detecting Community in Complex Networks

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Abstract

Discovering community structures is an important step to understanding the structure and dynamics of real-world networks in social science, biology and technology. In this paper, we develop a deep stochastic model based on non-negative matrix factorization to identify communities, in which there are two sets of parameters. One is the community membership matrix, of which the elements in a row correspond to the probabilities of the given node belongs to each of the given number of communities in our model, another is the community-community connection matrix, of which the element in the i-th row and j-th column represents the probability of there being an edge between a randomly chosen node from the i-th community and a randomly chosen node from the j-th community. The parameters can be evaluated by an efficient updating rule, and its convergence can be guaranteed. The community-community connection matrix in our model is more precise than the community-community connection matrix in traditional non-negative matrix factorization methods. Furthermore, the method called symmetric nonnegative matrix factorization, is a special case of our model. Finally, based on the experiments on both synthetic and real-world networks data, it can be demonstrated that our algorithm is highly effective in detecting communities.

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Notes

  1. Richard J. Bearman Peter S. & Harris Kathleen Mullan This work uses data from Add Health, a program project designed by Udry, funded by a Grant P01-HD31921 from the National Institute of Child Health, with cooperative funding from 17 other agencies. Special Acknowledgment is due Ronald R. Rindfuss Human Development, and 123 W. Franklin Street Chapel Hill NC 27516-2524 (addhealth@unc.edu) Barbara Entwisle for assistance in the original design. Persons interested in obtaining data files from Add Health should contact Add Health, Carolina Population Center.

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Acknowledgements

This work is supported by the National Nature Science Foundation of China (11271006), Independent Innovation Foundation of Shandong University (IFYT 14013), Shandong Provincial Natural Science Foundation (ZR2012GQ002, ZR2014AQ001).

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Authors and Affiliations

  1. School of Mathematics, Shandong University, No. 27 Shanda Nanlu, Jinan, 250100, Shandong, China

    Jingcheng Fu & Jianliang Wu

  2. Department of Computer Science and Engineering, Washington University in St. Louisa, St. Louis, MO, 63130, USA

    Jingcheng Fu

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  1. Jingcheng Fu
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  2. Jianliang Wu
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Correspondence to Jianliang Wu.

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Fu, J., Wu, J. A Deep Stochastic Model for Detecting Community in Complex Networks. J Stat Phys 166, 230–243 (2017). https://doi.org/10.1007/s10955-016-1681-y

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  • DOI: https://doi.org/10.1007/s10955-016-1681-y

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