Automated detection of edge clusters via an overfitted mixture prior

Most community detection methods focus on clustering actors with common features in a network. However, clustering edges offers a more intuitive way to understand the network structure in many real-life applications. Among the existing methods for network edge clustering, the majority are algorithmic, with the exception of the latent space edge clustering (LSEC) model proposed by Sewell (Journal of Computational and Graphical Statistics, 30(2), 390-405, 2021). LSEC was shown to have good performance in simulation and real-life data analysis, but fitting this model requires prior knowledge of the number of clusters and latent dimensions, which are often unknown to researchers. Within a Bayesian framework, we propose an extension to the LSEC model using a sparse finite mixture prior that supports automated selection of the number of clusters. We refer to our proposed approach as the automated LSEC or aLSEC. We develop a variational Bayes generalized expectation-maximization approach and a Hamiltonian Monte Carlo-within Gibbs algorithm for estimation. Our simulation study showed that aLSEC reduced run time by 10 to over 100 times compared to LSEC. Like LSEC, aLSEC maintains a computational cost that grows linearly with the number of actors in a network, making it scalable to large sparse networks. We developed the R package aLSEC which implements the proposed methodology.