(74e) Dimensionality Reduction of Dynamic Networks

A canonical problem in the field of dimensionality reduction is to efficiently capture, in some mathematical sense, the important information contained within a collection of high-dimensional vectors. This leads to a simplified description of the vectors that lends itself to faster computation and easier interpretability. Given the ongoing research into complex networks, we present techniques to extend these dimensionality reduction methods, in particular Diffusion Maps, to operate on a collection of graphs. This allows the researcher to obtain a reduced description of the network using only simulation data, and without analyzing the analytical equations that constitute the model. We illustrate Diffusion Maps' effectiveness in the context of both an epidemiological network model and a dynamic multigraph system. Computational challenges and promising future directions will also be discussed.