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：本文考虑图时间序列中异常检测的图信号处理问题。我们研究两个相关且互补的推断任务：检测时间序列中的异常图，以及检测时间上的异常顶点。我们通过调整基于统计原理的联合图推断方法来解决这些任务，具体采用*多重邻接谱嵌入*（MASE）。我们证明该方法对推断任务有效。此外，我们从可检测异常的潜在特性角度评估了方法的性能。进一步地，我们为该方法提供了理论依据并对其应用提出了见解。将方法应用于安然通信图和大规模商业搜索引擎图时间序列，我们的方法展示了其实用性，并识别出不仅限于大度数变化的异常顶点。