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Variational Bayesian Inference and Model Selection for the Stochastic Block Model with Irrelevant Vertices

Please always quote using this URN: urn:nbn:de:0297-zib-57003
  • Real World networks often exhibit a significant number of vertices which are sparsely and irregularly connected to other vertices in the network. For clustering theses networks with a model based algorithm, we propose the Stochastic Block Model with Irrelevant Vertices (SBMIV) for weighted net- works. We propose an original Variational Bayesian Expectation Maximiza- tion inference algorithm for the SBMIV which is an advanced version of our Blockloading algorithm for the Stochastic Block Model. We introduce a model selection criterion for the number of clusters of the SBMIV which is based on the lower variational bound of the model likelihood. We propose a fully Bayesian inference process, based on plausible informative priors, which is independent of other algorithms for preprocessing start values for the cluster assignment of vertices. Our inference methods allow for a multi level identification of irrelevant vertices which are hard to cluster reliably ac- cording to the SBM. We demonstrate that our methods improve on the normal Stochastic Block model by applying it to to Earthquake Networks which are an example of networks with a large number of sparsely and irregularly con- nected vertices.

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Author:Christian Tobias Willenbockel, Christof Schütte
Document Type:ZIB-Report
Tag:Clustering; Model Selection,; Networks; Noise; Stochastic Block Model; Variational Bayes EM; unsupervised classification
MSC-Classification:62-XX STATISTICS / 62Hxx Multivariate analysis [See also 60Exx] / 62H12 Estimation
62-XX STATISTICS / 62Hxx Multivariate analysis [See also 60Exx] / 62H30 Classification and discrimination; cluster analysis [See also 68T10]
Date of first Publication:2016/01/11
Series (Serial Number):ZIB-Report (16-01)
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