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：本文研究图时间序列中异常检测的图信号处理问题。我们探讨两个相关且互补的推理任务：检测时间序列中的异常图，以及检测时间异常顶点。我们通过改编基于统计原理的联合图推理方法来解决这些任务，具体采用多重邻接谱嵌入（MASE）。我们证明了该方法在上述推理任务中的有效性。此外，我们根据可检测异常的潜在性质评估了方法性能。我们进一步为该方法提供了理论依据，并深入阐释其应用原理。将所提方法应用于Enron通信图和大规模商业搜索引擎的图时间序列，结果表明了其适用性，并成功识别出超出单纯度变化的异常顶点。