Abstract The problem of quickest moving anomaly detection in networks is studied. Initially, the observations are generated according to a prechange distribution. At some unknown but deterministic time, an anomaly emerges in the network. At each time instant, one node is affected by the anomaly and receives data from a post-change distribution. The anomaly moves across the network, and the node that it affects changes with time. However, the trajectory of the moving anomaly is assumed to be unknown. A discrete-time Markov chain is employed to model the unknown trajectory of the moving anomaly in the network. A windowed generalized likelihood ratio–based test is constructed and is shown to be asymptotically optimal. Other detection algorithms including the dynamic Shiryaev-Roberts test, a quickest change detection algorithm with recursive change point estimation, and a mixture cumulative sum (CUSUM) algorithm are also developed for this problem. Lower bounds on the mean time to false alarm are developed. Numerical results are further provided to compare their performances.

中文翻译：

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网络中移动异常检测的顺序算法

摘要 研究了网络中最快的移动异常检测问题。最初，观察是根据预变化分布生成的。在某个未知但确定的时间，网络中出现异常。在每一时刻，一个节点受异常影响并从更改后分布接收数据。异常在网络中移动，它影响的节点随时间变化。然而，假设移动异常的轨迹是未知的。采用离散时间马尔可夫链对网络中移动异常的未知轨迹进行建模。构建了一个基于窗口广义似然比的测试，并显示为渐近最优。其他检测算法包括动态 Shiryaev-Roberts 测试，针对该问题还开发了具有递归变化点估计的最快变化检测算法和混合累积和 (CUSUM) 算法。制定了平均误报时间的下限。进一步提供了数值结果以比较它们的性能。