Euclidean Mirrors and Dynamics in Network Time Series

Analyzing changes in network evolution is central to statistical network inference. We consider a dynamic network model in which each node has an associated time-varying low-dimensional latent vector of feature data, and connection probabilities are functions of these vectors. Under mild assumptions, the evolution of latent vectors exhibits low-dimensional manifold structure under a suitable distance. This distance can be approximated by a measure of separation between the observed networks themselves, and there exist Euclidean representations for underlying network structure, as characterized by this distance. These Euclidean representations, called Euclidean mirrors, permit the visualization of network dynamics and lead to methods for change point and anomaly detection in networks. We illustrate our methodology with real and synthetic data, and identify change points corresponding to massive shifts in pandemic policies in a communication network of a large organization. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.