Dynamic Time Warping

Dynamic time warping (DTW) is a well-known technique to find an optimal alignment between two given (time-dependent) sequences under certain restrictions (Fig. 4.1). Intuitively, the sequences are warped in a nonlinear fashion to match each other. Originally, DTW has been used to compare different speech patterns in automatic speech recognition, see [170]. In fields such as data mining and information retrieval, DTW has been successfully applied to automatically cope with time deformations and different speeds associated with time-dependent data.

In this chapter, we introduce and discuss the main ideas of classical DTW (Sect. 4.1) and summarize several modifications concerning local as well as global parameters (Sect. 4.2). To speed up classical DTW, we describe in Sect. 4.3 a general multiscale DTW approach. In Sect. 4.4, we show how DTW can be employed to identify all subsequence within a long data stream that are similar to a given query sequence (Sect. 4.4). A discussion of related alignment techniques and references to the literature can be found in Sect. 4.5.