Abstract

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.

Notes

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Graduation Date

2023

Semester

Spring

Advisor

Pensky, Marianna

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0009628; DP0027659

URL

https://purls.library.ucf.edu/go/DP0027659

Language

English

Release Date

May 2023

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

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Included in

Mathematics Commons

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