PHD Defense: Mark He
Community Detection in Multimodal Networks
Community detection on networks is a basic, yet powerful and ever-expanding set of methodologies that is useful in a variety of settings. This dissertation discusses a range of different community detection on networks with multiple and non-standard modalities. A major focus of analysis is on the study of networks spanning several layers, which represent relationships such as interactions over time, different facets of high-dimensional data. These networks may be represented by several different ways; namely the few-layer (i.e. longitudinal) case as well as the many-layer (time-series cases). In the first case, we develop a novel application of variational expectation maximization as an example of the top-down mode of simultaneous community detection and parameter estimation. In the second case, we use a bottom-up strategy of iterative nodal discovery for these longer time-series, abetted with the assumption of their structural properties. In addition, we explore significantly self-looping networks, whose features are inseparable from the inherent construction of spatial networks whose weights are reflective of distance information. These types of networks are used to model and demarcate geographical regions. We also describe some theoretical properties and applications of a method for finding communities in bipartite networks that are weighted by correlations between samples. We discuss different strategies for community detection in each of these different types of networks, as well as their implications for the broader contributions to the literature. In addition to the methodologies, we also highlight the types of data wherein these “non-standard” network structures arise and how they are fitting for the applications of the proposed methodologies: particularly spatial networks and multilayer networks. We apply the top-down and bottom-up community detection algorithms to data in the domains of demography, human mobility, genomics, climate science, psychiatry, politics, and neuroimaging. The expansiveness and diversity of these data speak to the flexibility and ubiquity of our proposed methods to all forms of relational data.