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Title: Spectral analysis of networks with latent space dynamics and signs Authors:  Joshua Cape - University of Pittsburgh (United States) [presenting]
Abstract: The problem of modeling and analyzing latent space dynamics in collections of networks is considered. Towards this end, we pose and study latent space generative models for signed networks that are amenable to inference via spectral methods. Permitting signs, rather than restricting to unsigned networks, enables richer latent space structure and permissible dynamic mechanisms that can be provably inferred via low-rank truncations of observed adjacency matrices. The treatment of and ability to recover latent space dynamics holds across different levels of granularity, namely, at the overall graph level, for communities of nodes, and even at the individual node level. We provide synthetic and real data examples to illustrate the effectiveness of methodologies and to corroborate the accompanying theory. The contributions complement an emerging statistical paradigm for random graph inference encompassing random dot product graphs and generalizations thereof.