Derivative Dynamic Time Warping

1 Introduction Time series are a ubiquitous form of data occurring in virtually every scientific discipline. A common task with time series data is comparing one sequence with another. In some domains a very simple distance measure, such as Euclidean distance will suffice. However, it is often the case that two sequences have the approximately the same overall component shapes, but these shapes do not line up in X-axis. Figure 1 shows this with a simple example. In order to find the similarity between such sequences, or as a preprocessing step before averaging them, we must “warp” the time axis of one (or both) sequences to achieve a better alignment. Dynamic time warping (DTW), is a technique for efficiently achieving this warping. In addition to data mining (Keogh & Pazzani 2000, Yi et. al. 1998, Berndt & Clifford 1994), DTW has been used in gesture recognition (Gavrila & Davis 1995), robotics (Schmill et. al 1999), speech processing (Rabiner & Juang 1993), manufacturing (Gollmer & Posten 1995) and medicine (Caiani et. al 1998).