Generalized Dynamic Time Warping: Unleashing the Warping Power Hidden in Point-Wise Distances

Domain-specific distances preferred by analysts for exploring similarities among time series tend to be "point-to-point" distances. Unfortunately, this point-wise nature limits their ability to perform meaningful comparisons between sequences of different lengths and with temporal mis-alignments. Analysts instead need "elastic" alignment tools such as Dynamic Time Warping (DTW) to perform such flexible comparisons. However, the existing alignment tools are limited in that they do not incorporate diverse distances. To address this shortcoming, our work introduces the first conceptual framework called Generalized Dynamic Time Warping (GDTW) that supports now alignment (warping) of a large array of domain-specific distances in a uniform manner. While the classic DTW and its prior extensions focus on the Euclidean Distance, our GDTW is the first method that generalizes the ubiquitous DTW and "extends" its warping capabilities to a rich diversity of point-to-point distances. Based on our GDTW paradigm that preserves the efficiency of the dynamic programming paradigm of DTW, we design an abstraction that implemented by our GDTW Design Tool enables analysts to "warp" new distances with little programming effort. Through extensive evaluation studies on 85 real public domain benchmark datasets, we show that our newly warped distances offer higher classification accuracy than the previously available distances for the majority of these datasets. Further, our case study on heart arrhythmia data illustrates the utility of the new distances enabled by our GDTW warping methodology.