FastDTW: Toward Accurate Dynamic Time Warping in Linear Time and Space

The dynamic time warping (DTW) algorithm is able to find the optimal alignment between two time series. It is often used to determine time series similarity, classification, and to find corresponding regions between two time series. DTW has a quadratic time and space complexity that limits its use to only small time series data sets. In this paper we introduce FastDTW, an approximation of DTW that has a linear time and space complexity. FastDTW uses a multilevel approach that recursively projects a solution from a coarse resolution and refines the projected solution. We prove the linear time and space complexity of FastDTW both theoretically and empirically. We also analyze the accuracy of FastDTW compared to two other existing approximate DTW algorithms: Sakoe-Chuba Bands and Data Abstraction. Our results show a large improvement in accuracy over the existing methods.