sDTW: Computing DTW Distances using Locally Relevant Constraints based on Salient Feature Alignments

Many applications generate and consume temporal data and retrieval of time series is a key processing step in many application domains. Dynamic time warping (DTW) distance between time series of size N and M is computed relying on a dynamic programming approach which creates and fills an N × M grid to search for an optimal warp path. Since this can be costly, various heuristics have been proposed to cut away the potentially unproductive portions of the DTW grid. In this paper, we argue that time series often carry structural features that can be used for identifying locally relevant constraints to eliminate redundant work. Relying on this observation, we propose salient feature based sDTW algorithms which first identify robust salient features in the given time series and then find a consistent alignment of these to establish the boundaries for the warp path search. More specifically, we propose alternative fixed core&adaptive width, adaptive core&fixed width, and adaptive core&adaptive width strategies which enforce different constraints reflecting the high level structural characteristics of the series in the data set. Experiment results show that the proposed sDTW algorithms help achieve much higher accuracy in DTW computation and time series retrieval than fixed core & fixed width algorithms that do not leverage local features of the given time series.