Detecting changes in data streams is a vital task in many applications. There is increasing interest in changepoint detection in the online setting, to enable real-time monitoring and support prompt responses and informed decision-making. Many approaches assume stationary sequences before encountering an abrupt change in the mean or variance. Notably less attention has focused on the challenging case where the monitored sequences exhibit trend, periodicity and seasonality. Dynamic mode decomposition is a data-driven dimensionality reduction technique that extracts the essential components of a dynamical system. We propose a changepoint detection method that leverages this technique to sequentially model the dynamics of a moving window of data and produce a low-rank reconstruction. A change is identified when there is a significant difference between this reconstruction and the observed data, and we provide theoretical justification for this approach. Extensive simulations demonstrate that our approach has superior detection performance compared to other methods for detecting small changes in mean, variance, periodicity, and second-order structure, among others, in data that exhibits seasonality. Results on real-world datasets also show excellent performance compared to contemporary approaches.

翻译：数据流中的变化检测是众多应用中的关键任务。在线环境下的变点检测日益受到关注，以实现实时监测并支持快速响应与知情决策。许多方法假设序列在遭遇均值或方差的突变前是平稳的。对于监测序列呈现趋势性、周期性和季节性的挑战性情形，现有研究关注明显不足。动态模态分解是一种数据驱动的降维技术，能够提取动力系统的本质成分。我们提出一种变点检测方法，利用该技术对滑动数据窗口的动态特性进行序贯建模，并生成低秩重构。当重构数据与观测数据存在显著差异时，即判定发生变点，我们为此方法提供了理论依据。大量仿真实验表明，在具有季节性的数据中，针对均值、方差、周期性和二阶结构等特征的微小变化，本方法的检测性能优于其他对比方法。真实数据集上的实验结果也显示，相较于现有方法，本方法具有优异的性能表现。