Advances in Data Analysis, Data Handling and Business Intelligence
Part of the series Studies in Classification, Data Analysis, and Knowledge Organization pp 229-239
Bayesian Methods for Graph Clustering
- Pierre LatoucheAffiliated withLaboratoire Statistique et Génome, UMR CNRS 8071-INRA 1152-UEVE Email author
- , Etienne Birmelé
- , Christophe Ambroise
Abstract
Networks are used in many scientific fields such as biology, social science, and information technology. They aim at modelling, with edges, the way objects of interest, represented by vertices, are related to each other. Looking for clusters of vertices, also called communities or modules, has appeared to be a powerful approach for capturing the underlying structure of a network. In this context, the Block-Clustering model has been applied on random graphs. The principle of this method is to assume that given the latent structure of a graph, the edges are independent and generated from a parametric distribution. Many EM-like strategies have been proposed, in a frequentist setting, to optimize the parameters of the model. Moreover, a criterion, based on an asymptotic approximation of the Integrated Classification Likelihood (ICL), has recently been derived to estimate the number of classes in the latent structure. In this paper, we show how the Block-Clustering model can be described in a full Bayesian framework and how the posterior distribution, of all the parameters and latent variables, can be approximated efficiently applying Variational Bayes (VB). We also propose a new non-asymptotic Bayesian model selection criterion. Using simulated data sets, we compare our approach to other strategies. We show that our criterion can outperform ICL.
Keywords
Bayesian model selection Block-clustering model Integrated classification likelihood Random graphs Variational Bayes Variational EMReference tools
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- Title
- Bayesian Methods for Graph Clustering
- Book Title
- Advances in Data Analysis, Data Handling and Business Intelligence
- Book Subtitle
- Proceedings of the 32nd Annual Conference of the Gesellschaft für Klassifikation e.V., Joint Conference with the British Classification Society (BCS) and the Dutch/Flemish Classification Society (VOC), Helmut-Schmidt-University, Hamburg, July 16-18, 2008
- Pages
- pp 229-239
- Copyright
- 2010
- DOI
- 10.1007/978-3-642-01044-6_21
- Print ISBN
- 978-3-642-01043-9
- Online ISBN
- 978-3-642-01044-6
- Series Title
- Studies in Classification, Data Analysis, and Knowledge Organization
- Series ISSN
- 1431-8814
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Keywords
-
- Bayesian model selection
- Block-clustering model
- Integrated classification likelihood
- Random graphs
- Variational Bayes
- Variational EM
- Industry Sectors
- eBook Packages
- Editors
-
- Andreas Fink (ID1)
- Berthold Lausen (ID2)
- Wilfried Seidel (ID3)
- Alfred Ultsch (ID4)
- Editor Affiliations
-
- ID1. Universität der Bundeswehr, Fak. Wirtschafts-/Sozialwissenschaften, Helmut-Schmidt-Universität
- ID2. Dept. Mathematical Sciences, University of Essex
- ID3. Universität der Bundeswehr, Fak. Wirtschafts-/Sozialwissenschaften, Helmut-Schmidt-Universität
- ID4. FB 12 Mathematik und Informatik, Datenbionik AG, Universität Marburg
- Authors
- Author Affiliations
-
- 1. Laboratoire Statistique et Génome, UMR CNRS 8071-INRA 1152-UEVE, 91000, Evry, France
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