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.
Author: | Christian Tobias Willenbockel, Christof Schütte |
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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) |
ISSN: | 1438-0064 |