Bayesian Analysis

Mixed Membership Stochastic Blockmodels for Heterogeneous Networks

Weihong Huang, Yan Liu, and Yuguo Chen

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Abstract

Heterogeneous networks are useful for modeling complex systems that consist of different types of objects. However, there are limited statistical models to deal with heterogeneous networks. In this paper, we propose a statistical model for community detection in heterogeneous networks. We formulate a heterogeneous version of the mixed membership stochastic blockmodel to accommodate heterogeneity in the data and the content dependent property of the pairwise relationship. We also apply a variational algorithm for posterior inference. The proposed procedure is shown to be consistent for community detection under mixed membership stochastic blockmodels for heterogeneous networks. We demonstrate the advantage of the proposed method in modeling overlapping communities and multiple memberships through simulation studies and applications to a real data set.

Article information

Source
Bayesian Anal., Advance publication (2018), 26 pages.

Dates
First available in Project Euclid: 19 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.ba/1560909813

Digital Object Identifier
doi:10.1214/19-BA1163

Keywords
clustering community detection heterogeneous network mixed membership model stochastic blockmodel variational algorithm

Rights
Creative Commons Attribution 4.0 International License.

Citation

Huang, Weihong; Liu, Yan; Chen, Yuguo. Mixed Membership Stochastic Blockmodels for Heterogeneous Networks. Bayesian Anal., advance publication, 19 June 2019. doi:10.1214/19-BA1163. https://projecteuclid.org/euclid.ba/1560909813


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Supplemental materials

  • Supplementary Material for “Mixed Membership Stochastic Blockmodels for Heterogeneous Networks”. The supplementary material contains the details of the variational posterior inference, variational EM algorithm, and the proofs of theoretical results in Section 4.