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 and a large-scale commercial search engine time series of graphs, our approaches demonstrate their applicability and identify the anomalous vertices beyond just large degree change.

翻译：本文研究时序图中异常检测的图信号处理问题。我们探讨了两个相关且互补的推断任务：时间序列中异常图的检测，以及时间异常顶点的检测。我们通过调整基于统计原则的联合图推断方法（具体为多重邻接谱嵌入，MASE）来解决这些任务。我们证明了该方法在推断任务中的有效性，并进一步从可检测异常的基本性质角度评估了其性能。此外，我们为该方法提供了理论依据并深入阐释了其应用原理。将本方法应用于Enron通信图和大规模商业搜索引擎的时序图，实验结果表明了其适用性，并成功识别出不仅限于度数突变的异常顶点。