Unsupervised concept drift detection for time series on Riemannian manifolds

Concept drifts generally refer to the changing of statistical characteristics of non-stationary series over time, which considerably affect the analysis of time series including prediction, anomaly detection and classification, etc. However, since the external noise interference and internal uncertainty of time series, it is still an open problem to detect the occurrence of concept drifts timely and effectively in real applications. In this article, based on Riemannian manifolds and statistical process control, we propose a novel online algorithm for the concept drift detection of time series. Using the online segmentations with multiple sliding windows, phase space reconstruction of time series is implemented, based on which multi-scale features of series data are calculated. By means of information geometry theory, the obtained features are projected into Riemannian manifolds for the evading of noise interference and structural redundancy in the time series. Finally, with statistical process control, the detection of concept drifts is implemented. The experimental results reveal the promising detection performances verified by both artificial data sets and real-life data sets.