Dear All,

We have the pleasure thanks to the support of the ESSEC IDS dpt, Institut des Actuaires, LabEx MME-DII, the group BFA (SFdS), to invite you to the seminar by:

Graph clustering is the task of partitioning a collection of observed networks into groups of similar networks. Clustering requires the comparison of graphs and the definition of a notion of graph similarity, which is challenging as networks are complex objects and possibly of different sizes. Our goal is to obtain a clustering where networks in the same cluster have similar global topology. We propose a model-based clustering approach based on a novel finite mixture model of random graph models, such that the clustering task is recast as an inference problem. To model individual networks the popular stochastic block model is used since it accommodates heterogeneous graphs and its parameters are readily interpretable. Moreover, we develop a hierarchical agglomerative clustering algorithm that aims at maximizing the so-called integrated classification likelihood criterion. Our greedy hill-climbing algorithm starts by treating each network as a singleton cluster and then performs successive merges of clusters until the best clustering is achieved. When merging two clusters, the label-switching problem in the stochastic block model raises an issue. Precisely, we have to match block labels of two stochastic block models. To address this problem we propose a tool based on the graphon function and a new distance measure for the comparison of stochastic block models.