A Gaussian process based online change detection algorithm for monitoring periodic time series

Online time series change detection is a critical component of many monitoring systems, such as space and air-borne remote sensing instruments, cardiac monitors, and network traffic profilers, which continuously analyze observations recorded by sensors. Data collected by such sensors typically has a periodic component. Most existing time series change detection methods are not directly applicable to handle such data, either because they are not designed to handle periodic time series or because they cannot operate in an online mode. We propose an online change detection algorithm which can handle periodic time series. The algorithm uses a Gaussian process based non-parametric time series prediction model and monitors the difference between the predictions and actual observations within a statistical control chart framework to identify changes. A key challenge in using Gaussian process in an online mode is the need to solve a large system of equations involving the associated covariance matrix which grows with every time step. The proposed algorithm exploits the special structure of the covariance matrix and can analyze a time series of length T in O(T²) time while maintaining a O(T) memory footprint, compared to O(T⁴) time and O(T²) memory requirement of standard matrix manipulation methods. We experimentally demonstrate the superiority of the proposed algorithm over several existing time series change detection algorithms on a set of synthetic and real time series. Finally, we illustrate the effectiveness of the proposed algorithm for identifying land use land cover changes using Normalized Difference Vegetation Index (NDVI) data collected for an agricultural region in Iowa state, USA. Our algorithm is able to detect different types of changes in a NDVI validation data set (with ≈ 80% accuracy) which occur due to crop type changes as well as natural disasters.