This dissertation 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 common particular cases, where layers of the network follow the Stochastic Block Model (SBM) and Degree Corrected Block Model (DCBM), this setting implies that the groups of layers have common community structures but all matrices of block connection probabilities can be different. For DCBM, each group can also equip with nodes' specific weights. We refer to this two versions as the DIMPLE model and the DIMPLE-DECOR model. While the DIMPLE-GDPG model generalizes the COmmon Subspace Independent Edge (COSIE) random graph model, 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, the checker-board model as well as the Mixture Multilayer Stochastic Block Model (MMLSBM) as particular cases). This dissertation introduces 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 also consider applications of the DIMPLE models to real-life data, and its comparison with the MMLSBM. And the DIMPLE model with its SBM-imposed structures provided better descriptions of the organization of layers than the ones obtained on the basis of the MMLSBM setting.
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Doctor of Philosophy (Ph.D.)
College of Sciences
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Wang, Yaxuan, "Clustering of Diverse Multiplex Networks" (2023). Electronic Theses and Dissertations, 2020-. 1692.