图时间序列中用于异常检测的局部性统计量
Locality statistics for anomaly detection in time series of graphs
AI总结：
本文针对随机块模型时间序列的变点检测，分析两类基于局部性统计量的扫描统计量，推导其极限分布与功效，并通过理论、合成数据和 Enron 语料库比较其容许性。
摘要：
在新兴的图信号处理学科的许多应用中，检测动态网络或图时间序列中变点的能力正成为一项日益重要的任务。本文依据生成式潜在位置模型，将变点检测表述为一个假设检验问题，并重点研究 Stochastic Block Model（随机块模型）时间序列这一特殊情形。我们分析了两类扫描统计量，它们基于文献中提出的不同底层局部性统计量。本文的主要贡献是推导了这些相互竞争的扫描统计量的极限分布和功效特征。我们在理论上、合成数据上以及 Enron 电子邮件语料库上对性能进行了比较。结果表明，在一种简单情形下两种统计量都是容许的，而在第二种情形下其中一种统计量是不容许的。
英文摘要：
The ability to detect change-points in a dynamic network or a time series of graphs is an increasingly important task in many applications of the emerging discipline of graph signal processing. This paper formulates change-point detection as a hypothesis testing problem in terms of a generative latent position model, focusing on the special case of the Stochastic Block Model time series. We analyze two classes of scan statistics, based on distinct underlying locality statistics presented in the literature. Our main contribution is the derivation of the limiting distributions and power characteristics of the competing scan statistics. Performance is compared theoretically, on synthetic data, and on the Enron email corpus. We demonstrate that both statistics are admissible in one simple setting, while one of the statistics is inadmissible a second setting.
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