Detection of Emergent Anomalous Structure in Functional Data

Motivated by an example arising from digital networks, we propose a novel approach for detecting the emergence of anomalies in functional data. In contrast to classical functional data approaches, which detect anomalies in completely observed curves, the proposed approach seeks to identify anomalies sequentially as each point on the curve is received. The new method, the Functional Anomaly Sequential Test (FAST), captures the common profile of the curves using Principal Differential Analysis and uses a form of CUSUM test to monitor a new functional observation as it emerges. Various theoretical properties of the procedure are derived. The performance of FAST is then assessed on both simulated and telecommunications data.

受数字网络相关实例的启发，我们提出了一种用于检测函数型数据（functional data）异常出现的新颖方法。与经典函数型数据方法仅在整条曲线完全观测后再检测异常不同，本文所提方法可在曲线各点被依次接收的过程中，对异常进行顺序识别。该新方法名为函数型异常顺序检验（Functional Anomaly Sequential Test，FAST），它通过主微分分析（Principal Differential Analysis）捕捉曲线的共性轮廓，并借助累积和检验（CUSUM test）的变体，对逐步生成的新函数型观测值进行监控。本研究推导了该检验流程的多项理论性质。随后，我们通过模拟数据与电信数据集，对FAST的性能进行了评估。