Bayesian clustering of block structured relational data

The discovery of latent information in large-scale databases has become a major problem of information technology and statistics in the recent years. The investigation of relational data, e.g. the structures of graphs is an important field of this problem. One notable task is the clustering of the nodes of the graph. This means the discovery of cohesive groups and the modelling of the cohesion. Bayesian networks have become the most popular tools for modelling data having unobserved or latent variables, since are able to represent the causal relations between the latent and the observable variables. There are several inference methods for these networks, but they provide only general frameworks. The particular cases are depending on the chosen model, the distribution of the random variables, and in many cases they are not tractable. This thesis reviews the probabilistic methods of relational data modelling and the Bayesian inference procedures that are able to cluster and discover the latent structures of (occasionally huge) graphs. Based on the previous methods a new generative model is proposed for clustering graphs. For the estimation of the model parameters a Markov Chain Monte Carlo (MCMC) algorithm is used, by implementing two different type of samplers. The new method is compared to the previous algorithms. Small graphs are investigated with it in order to choose the best parameters and to measure the clustering efficiency. Based on the experiments, the new model turns out to be more efficient than the foregoer methods. Finally, the new tool is used on a real, large-sized dataset.