The deep latent position topic model for clustering and representation of networks with textual edges

Numerical interactions leading to users sharing textual content published by others are naturally represented by a network where the individuals are associated with the nodes and the exchanged texts with the edges. To understand those heterogeneous and complex data structures, clustering nodes into homogeneous groups as well as rendering a comprehensible visualization of the data is mandatory. To address both issues, we introduce Deep-LPTM, a model-based clustering strategy relying on a variational graph auto-encoder approach and a probabilistic model to characterize the discussion topics. Deep-LPTM allows to build a joint representation of the nodes and the edges in two embedding spaces. The parameters are inferred using a variational inference algorithm. We also introduce IC2L, a model selection criterion specifically designed to choose models with relevant clustering and visualization properties. An extensive benchmark study on synthetic data is provided. In particular, we find that Deep-LPTM better recovers the partitions of the nodes than the state-of-the-art ETSBM and STBM. Eventually, the emails of the Enron company are analyzed and visualizations of the results are presented, with meaningful highlights of the graph structure.