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Title: Spectral methods for multiplex networks: An introduction to unfolded spectral embedding Authors:  Andrew Jones - University of Bristol (United Kingdom) [presenting]
Abstract: As a generic model for a network, we consider a set of entities together with a function describing their pairwise interactions. In the case of a multiplex network, this function is vector-valued (with each component corresponding to a specific feature of the interaction), and thus we may naturally view such networks as 3-dimensional tensors. Building upon existing spectral methods for graph analysis, unfolded spectral embedding (USE) is a novel technique which exploits this tensor structure to allow us to identify behavioural trends among the underlying entities by aggregating across all layers of interaction, while simultaneously providing us with layer-by-layer representations for comparison. We will briefly introduce USE, discuss how it can be applied to multiplex analogues of stochastic blockmodel graphs (including some asymptotic results concerning the output of the embedding), and present examples of its use in studying real-world dynamic graph networks.