This paper considers the graph signal processing problem of anomaly detection in time series of graphs. We examine two related, complementary inference tasks: the detection of anomalous graphs within a time series, and the detection of temporally anomalous vertices. We approach these tasks via the adaptation of statistically principled methods for joint graph inference, specifically \emph{multiple adjacency spectral embedding} (MASE). We demonstrate that our method is effective for our inference tasks. Moreover, we assess the performance of our method in terms of the underlying nature of detectable anomalies. We further provide the theoretical justification for our method and insight into its use. Applied to the Enron communication graph, a large-scale commercial search engine time series of graphs, and a larval Drosophila connectome data, our approaches demonstrate their applicability and identify the anomalous vertices beyond just large degree change.

翻译：本文研究图时间序列中的异常检测这一图信号处理问题。我们探讨了两个相互关联、互为补充的推理任务：时间序列中异常图的检测，以及时序异常顶点的检测。我们通过调整具有统计原理的联合图推理方法来解决这些任务，特别是采用多重邻接谱嵌入（MASE）方法。实验证明，该方法对我们的推理任务具有显著效果。此外，我们还从可检测异常的基本性质角度评估了该方法的性能。我们进一步提供了该方法的理论依据并深入阐释其应用机制。在安然通信图、大规模商业搜索引擎图时间序列以及果蝇幼虫连接组数据上的应用表明，我们的方法不仅具有实际适用性，还能识别超出单纯度值变化的异常顶点。