Clustering of Diverse Multiplex Networks

The paper introduces the DIverse MultiPLEx (DIMPLE) network model where all layers of the network have the same collection of nodes and are equipped with the Stochastic Block Models (SBM). In addition, all layers can be partitioned into groups with the same community structures, although the layers in the same group may have different matrices of block connection probabilities. The DIMPLE model generalizes a multitude of papers that study multilayer networks with the same community structures in all layers (which include the tensor block model and the checker-board model as particular cases), as well as the Mixture Multilayer Stochastic Block Model (MMLSBM), where the layers in the same group have identical matrices of block connection probabilities. Since the techniques from either of the above mentioned groups cannot be applied to the DIMPLE model, we introduce novel algorithms for the between-layer and the within-layer clustering. We study the accuracy of those algorithms, both theoretically and via computer simulations. Finally, we show how our between-layer clustering algorithm can be extended to the Heterogeneous Multiplex Random Dot-Product Graph model, which generalizes the COmmon Subspace Independent Edge (COSIE) random graph model developed in Arroyo et al. (Journ. Machine Learn. Res., 2021).