Graph Clustering by Maximizing Statistical Association Measures

We are interested in objective functions for clustering undirected and unweighted graphs. Our goal is to define alternatives to the popular modularity measure. To this end, we propose to adapt statistical association coefficients, which traditionally measure the proximity between partitions, for graph clustering. Our approach relies on the representation of statistical association measures in a relational formulation which uses the adjacency matrices of the equivalence relations underlying the partitions. We show that graph clustering can then be solved by fitting the graph with an equivalence relation via the maximization of a statistical association coefficient. We underline the connections between the proposed framework and the modularity model. Our theoretical work comes with an empirical study on computer-generated graphs. Our results show that the proposed methods can recover the community structure of a graph similarly or better than the modularity.