Change Detection in Time Series Data Using Wavelet Footprints

Detecting changes in time series data is an important data analysis task with application in various scientific domains. In this paper, we propose a novel approach to address the problem of change detection in time series data, which can find both the amplitude and degree of changes. Our approach is based on wavelet footprints proposed originally by the signal processing community for signal compression. We, however, exploit the properties of footprints to efficiently capture discontinuities in a signal. We show that transforming time series data using footprint basis up to degree D generates nonzero coefficients only at the change points with degree up to D. Exploiting this property, we propose a novel change detection query processing scheme which employs footprint-transformed data to identify change points, their amplitudes, and degrees of change efficiently and accurately. We also present two methods for exact and approximate transformation of data. Our analytical and empirical results with both synthetic and real-world data show that our approach outperforms the best known change detection approach in terms of both performance and accuracy. Furthermore, unlike the state of the art approaches, our query response time is independent from the number of change points in the data and the user-defined change threshold.