Dynamic networks consist of a sequence of time-varying networks, and it is of great importance to detect the network change points. Most existing methods focus on detecting abrupt change points, necessitating the assumption that the underlying network probability matrix remains constant between adjacent change points. This paper introduces a new model that allows the network probability matrix to undergo continuous shifting, while the latent network structure, represented via the embedding subspace, only changes at certain time points. Two novel statistics are proposed to jointly detect these network subspace change points, followed by a carefully refined detection procedure. Theoretically, we show that the proposed method is asymptotically consistent in terms of change point detection, and also establish the impossibility region for detecting these network subspace change points. The advantage of the proposed method is also supported by extensive numerical experiments on both synthetic networks and a UK politician social network.

翻译：动态网络由一系列时变网络构成，检测网络变点具有重要实际意义。现有方法大多聚焦于突变型变点的检测，需假设相邻变点间的隐含网络概率矩阵保持恒定。本文提出一种新模型，允许网络概率矩阵连续漂移，而通过嵌入子空间表征的隐含网络结构仅在某些特定时间点发生变化。为联合检测这些网络子空间变点，我们构建了两项新型统计量，并辅以经精细优化的检测流程。理论上，我们证明该方法在变点检测方面具有渐近一致性，并建立了网络子空间变点检测的不可行区域。通过合成网络与英国政客社交网络的大量数值实验，进一步验证了所提方法的优越性。