Euclidean mirrors and first-order changepoints in network time series

TL;DR

This paper introduces a model for network time series using Euclidean space representations, defining first-order changepoints, and demonstrating that spectral methods can accurately localize these shifts in network evolution.

Contribution

It presents a novel Euclidean mirror model for network time series and proves spectral methods can detect changepoints even with continuous but varying graph distributions.

Findings

Spectral estimates localize changepoints effectively.

Model captures significant shifts in network evolution.

Validated with simulated and real organoid network data.

Abstract

We describe a model for a network time series whose evolution is governed by an underlying stochastic process, known as the latent position process, in which network evolution can be represented in Euclidean space by a curve, called the Euclidean mirror. We define the notion of a first-order changepoint for a time series of networks, and construct a family of latent position process networks with underlying first-order changepoints. We prove that a spectral estimate of the associated Euclidean mirror localizes these changepoints, even when the graph distribution evolves continuously, but at a rate that changes. Simulated and real data examples on organoid networks show that this localization captures empirically significant shifts in network evolution.