Dynamic Time Warping Based on Cubic Spline Interpolation for Time Series Data Mining

Dynamic time warping (DTW) and derivative dynamic time warping (DDTW) are two robust distance measures for time series, which allows similar shapes to match even if they are out of phase in the time axis. In this paper, we propose a novel dynamic time warping based on cubic spline interpolation (SIDTW) to improve the performance. The derivative of every point of time series is calculated by cubic spline interpolation and is used to replace the estimated derivatives in DDTW. After interpolation we use derivative-based sequences to represent the original time series, which is better to describe the trend of the original time series and more reasonable to warp. Meanwhile, we empirically point out that the quality of similarity measure for the three warping methods is nothing to do with the amount of warping. We experimentally perform the proposed method and compare with the existing ones, which demonstrates that in most cases our approach not only can produce much less singularities and obtain the best warping path with shorter length but also is an alternative version of DTW when time series datasets are not suitable for DTW to be measured.