AI 中文总结
该研究针对时间依赖网络序列，提出基于形成与消失事件矩阵及展开邻接谱嵌入的异常检测方法，在自回归随机点积图等模型上有理论保证，经模拟和真实数据集验证有效。
AI 中文摘要
我们研究时间依赖网络序列中的异常检测。仅基于邻接矩阵的方法（广泛用于静态网络）可能会遗漏边的演化方式变化。我们转而将每对连续网络表示为单独的形成事件矩阵和消失事件矩阵，并使用展开邻接谱嵌入对所得矩阵序列进行嵌入。将这些嵌入与平稳基线进行比较，可得到顶点级和网络级统计量，用于检测异常转换并识别其是否涉及形成、消失或两者。对于自回归随机点积图，我们建立了转换事件嵌入的逐行一致性，并推导了顶点级和网络级检测以及异常顶点集精确恢复的高概率保证。该理论将顶点自身的位移与其他顶点造成的干扰以及自回归记忆分离开来。我们量化了早期异常留下的记忆，表明在转换机制返回基线后，该记忆呈几何衰减，并给出了其可忽略的条件。度校正随机块模型扩展可实现精确社区恢复，并提供社区重新分配、中心偏移、分裂和合并异常统计量，具有高概率检测和恢复保证。模拟以及对国际贸易数据集和小学接触网络的应用，说明了所提方法的性能，揭示了COVID-19期间由消失驱动的贸易下降后跟随由形成驱动的复苏，以及班级间的临时合并型混合。
英文摘要
We study anomaly detection in temporally dependent network sequences. Methods based only on adjacency matrices, which are widely used for static networks, can miss changes in the way edges evolve. We instead represent each pair of consecutive networks by separate formation and dissolution event matrices, and embed the resulting matrix sequences using unfolded adjacency spectral embedding. Comparing these embeddings against a stationary baseline yields vertex- and network-level statistics that detect an anomalous transition and identify whether it involves formation, dissolution, or both. For autoregressive random dot product graphs, we establish uniform rowwise consistency of the transition-event embeddings and derive high-probability guarantees for vertex- and network-level detection and exact recovery of the anomalous vertex set. The theory separates a vertex's own displacement from interference caused by other vertices and from autoregressive memory. We quantify the memory left by an earlier anomaly, show that it decays geometrically after the transition mechanism returns to baseline, and give conditions under which it is negligible. A degree-corrected stochastic block model extension gives exact community recovery and provides community-reassignment, centre-shift, split, and merge anomaly statistics with high-probability detection and recovery guarantees. Simulations and applications to an international trade dataset and a primary-school contact network illustrate the performance of the proposed method, revealing a dissolution-driven trade decline followed by formation-driven recovery during COVID-19 and temporary merge-type mixing between school classes.
