TY - GEN A1 - Willenbockel, Christian Tobias A1 - Schütte, Christof T1 - Variational Bayesian Inference and Model Selection for the Stochastic Block Model with Irrelevant Vertices N2 - 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. T3 - ZIB-Report - 16-01 KW - Clustering KW - Variational Bayes EM KW - Model Selection, KW - Stochastic Block Model KW - Networks KW - unsupervised classification KW - Noise Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57003 SN - 1438-0064 ER - TY - GEN A1 - Willenbockel, Christian Tobias A1 - Schütte, Christof T1 - A Variational Bayesian Algorithm for Clustering of Large and Complex Networks N2 - We propose the Blockloading algorithm for the clustering of large and complex graphs with tens of thousands of vertices according to a Stochastic Block Model (SBM). Blockloading is based on generalized Variational Bayesian EM (VBEM) schemes and works for weighted and unweighted graphs. Existing Variational (Bayesian) EM methods have to consider each possible number of clusters sepa- rately to determine the optimal number of clusters and are prone to converge to local optima making multiple restarts necessary. These factors impose a severe restriction on the size and complexity of graphs these methods can handle. In con- trast, the Blockloading algorithm restricts restarts to subnetworks in a way that provides error correction of an existing cluster assignment. The number of clusters need not be specified in advance because Blockloading will return it as a result. We show that Blockloading outperforms all other variational methods regarding reliability of the results and computational efficiency. T3 - ZIB-Report - 15-25 KW - Clustering KW - Variational Bayes EM KW - Model Selection, KW - Stochastic Block Model KW - Networks KW - unsupervised classification Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54588 SN - 1438-0064 ER -