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Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering


Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.

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  1. i.e., we consider only node-attributed graphs throughout the paper.

  2. Non-regular models refer to the models that do not satisfy regularity conditions with BIC [4].

  3. The zero diagonal of \({\mathbf {X}}\) means no self-loops in the corresponding graph while symmetry means that the graph is undirected, in accordance with our focus on undirected simple graphs.

  4. The definition of our clustering requires as less edges as possible between distinct clusters.

  5. Multinomial and Dirichlet distributions are conjugate. As a special case, Bernoulli and Beta distributions are conjugate as well.

  6. The stick-breaking prior is a representation of the Dirichlet process and often used for variational inference. The Dirichlet process here is the distribution of a random probability measure over positive integers.

  7. That is, each prior is a uniform distribution over the components. This is reasonable given that we do not have any prior information on the proportion of different components and thus they are treated equally important.

  8. The corresponding assortativity coefficient is negative, \(r=-0.079\).


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The authors would like to thank the anonymous reviewers of the paper for their valuable comments that help significantly improve the quality of the paper.

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Correspondence to Zhiqiang Xu.

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Xu, Z., Cheng, J., Xiao, X. et al. Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering. Knowl Inf Syst 53, 239–268 (2017).

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  • Attributed graph clustering
  • Model selection
  • Dirichlet process
  • Factorized information criterion