Euclidean mirrors and dynamics in network time series

TL;DR

This paper introduces Euclidean mirrors, a method for visualizing and analyzing network evolution by embedding network data into Euclidean space, enabling change-point detection and anomaly identification in dynamic networks.

Contribution

The paper proposes Euclidean mirrors that approximate network structure in Euclidean space, facilitating visualization and classical analysis of network dynamics, including change-point detection.

Findings

Successfully identified change points related to pandemic policy shifts

Demonstrated the method on real and synthetic network data

Enabled visualization of network evolution in Euclidean space

Abstract

Analyzing changes in network evolution is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We consider a joint 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 time-varying evolution of the latent vectors exhibits low-dimensional manifold structure under a suitable notion of 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, at any given time. These Euclidean representations, called Euclidean mirrors, permit the visualization of network evolution and transform network inference questions such as change-point and anomaly detection into a classical setting. 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.