Online Changepoint Detection via Dynamic Mode Decomposition

TL;DR

This paper introduces a novel online changepoint detection method using dynamic mode decomposition, effectively identifying structural changes in data streams with complex seasonal patterns in real-time.

Contribution

It presents a new approach that leverages dynamic mode decomposition for online changepoint detection, especially in non-stationary, seasonal data.

Findings

Outperforms existing methods in detecting small changes in mean and variance.

Effective in identifying changes in periodicity and second-order structure.

Demonstrates superior performance on real-world seasonal datasets.

Abstract

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.