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.

翻译：本文描述了一种网络时间序列模型，其演化由潜在位置过程这一基础随机过程所控制，网络演化可通过一条称为欧几里得镜像的曲线在欧几里得空间中表示。我们定义了网络时间序列中一阶变点的概念，并构建了一类具有基础一阶变点的潜在位置过程网络。我们证明了相关欧几里得镜像的谱估计能够定位这些变点，即使在图分布连续演化但其速率发生变化的情况下亦然。基于类器官网络的模拟与真实数据示例表明，该定位方法能够捕捉网络演化中经验意义上显著的转变。