用于在线变点检测的校准持久拉普拉斯累积和
Online Change-Point Detection with Persistent Laplacian Features
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中文总结 AI 辅助
针对高维非线性时间序列在线变点检测，提出PL-CUSUM方法，将滑动窗口转为点云，用持久拉普拉斯谱构建监测分数，分析关键性能标准，给出阶段程序，实验表明其能稳定控制误报且检测性能有竞争力。
中文摘要 AI 辅助
我们提出了持久拉普拉斯累积和（PL-CUSUM），一种用于高维非线性时间序列的在线变点检测方法。该方法将滑动窗口转换为点云，并使用持久拉普拉斯谱为Page累积和（Page-CUSUM）递归构建监测分数。与仅基于持久同调摘要的检测器相比，PL-CUSUM进一步利用谱信息来捕获尺度内连通性和超越同调计数的几何结构。理论上，我们分析了两个关键性能标准：误报控制和检测延迟。我们推导了神谕检测器的误报延迟界，并表明插件白化分数在有限监测范围内仍能控制误报。方法上，我们提供了一个I/II阶段程序，在在线递归之前进行参数选择和控制限校准。在模拟系统和实际监测数据上的实验表明，PL-CUSUM提供了稳定的误报控制和有竞争力的检测性能。
英文摘要
Online change-point detection in high-dimensional nonlinear time series faces two challenges. The underlying distributions are difficult to model, and state changes are difficult to characterize. We propose persistent Laplacian cumulative sum (PL-CUSUM) to address these challenges. PL-CUSUM maps delay-embedded sliding windows to point clouds. It extracts persistent Betti vectors and the positive spectra of persistent Laplacians from the same Vietoris-Rips filtration. A ridge-whitened projection converts these features into a scalar score. Page's CUSUM recursion then accumulates this score over time. The positive spectra capture within-scale connectivity and geometric information that persistent Betti vectors do not record. Under a finite-support local model, we prove that the oracle upper bound on detection delay and a local minimax lower bound have the same order. This common order is the logarithm of the average run length constraint divided by the squared ridge-whitened separation. We also establish finite-horizon false-alarm and expected-delay bounds for plug-in whitened scores under weak dependence within each state. The method has two phases. Phase I estimates the projection parameters, selects the feature configuration, and calibrates the control limit. Phase II updates the resulting CUSUM statistic online. Experiments on simulated and real monitoring data show stable false-alarm control and competitive detection performance.
