Clustering of Diverse Multiplex Networks

Abstract: The paper introduces the DIverse MultiPLEx Generalized Dot Product Graph (DIMPLE-GDPG) network model where all layers of the network have the same collection of nodes and follow the Generalized Dot Product Graph (GDPG) model. In addition, all layers can be partitioned into groups such that the layers in the same group are embedded in the same ambient subspace but otherwise all matrices of connection probabilities can be different. In a common particular case, where layers of the network follow the Stochastic Block Model (SBM), this setting implies that the groups of layers have common community structures but all matrices of block connection probabilities can be different. We refer to this version as the DIMPLE model. While the DIMPLE-GDPG model generalizes the COmmon Subspace Independent Edge (COSIE) random graph model developed in \cite{JMLR:v22:19-558}, the DIMPLE model includes a wide variety of SBM-equipped multilayer network models as its particular cases. In the paper, we introduce novel algorithms for the recovery of similar groups of layers, for the estimation of the ambient subspaces in the groups of layers in the DIMPLE-GDPG setting, and for the within-layer clustering in the case of the DIMPLE model. We study the accuracy of those algorithms, both theoretically and via computer simulations. The advantages of the new models are demonstrated using real data examples.