Block modelling in dynamic networks with non-homogeneous Poisson processes and exact ICL
This work addresses the challenge of clustering nodes in dynamic networks for researchers in network analysis, representing an incremental improvement by combining existing methods with new regularization techniques.
The authors tackled the problem of modeling dynamic networks by developing a block model where interactions are counted using non-homogeneous Poisson processes, with nodes belonging to hidden clusters. They derived an exact integrated classification likelihood criterion for simultaneous estimation of cluster memberships and number of clusters, and proposed a regularized version to address over-fitting, validated through experiments on real and simulated data.
We develop a model in which interactions between nodes of a dynamic network are counted by non homogeneous Poisson processes. In a block modelling perspective, nodes belong to hidden clusters (whose number is unknown) and the intensity functions of the counting processes only depend on the clusters of nodes. In order to make inference tractable we move to discrete time by partitioning the entire time horizon in which interactions are observed in fixed-length time sub-intervals. First, we derive an exact integrated classification likelihood criterion and maximize it relying on a greedy search approach. This allows to estimate the memberships to clusters and the number of clusters simultaneously. Then a maximum-likelihood estimator is developed to estimate non parametrically the integrated intensities. We discuss the over-fitting problems of the model and propose a regularized version solving these issues. Experiments on real and simulated data are carried out in order to assess the proposed methodology.