# Euclidean mirrors and first-order changepoints in network time series

arXiv: https://arxiv.org/abs/2405.11111 · HTML: https://mlsanity.com/paper/2405.11111/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2024.

## Built on by (most cited first, 4 of 4)

- [Multiscale Euclidean Network Trajectories: Second-Moment Geometry, Attribution, and Change Points](https://mlsanity.com/paper/2605.04589/) (2026)
- [Control Charts for Multi-agent Systems](https://mlsanity.com/paper/2605.11135/) (2026)
- [Optimizing the Induced Correlation in Omnibus Joint Graph Embeddings](https://mlsanity.com/paper/2409.17544/) (2024)
- [Geodesics of Dynamic Graphs for Regime Change Detection](https://mlsanity.com/paper/2606.07151/) (2026)

## Abstract (arXiv)

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.