Early Abandoning and Pruning for Elastic Distances including Dynamic Time Warping

Abstract: Nearest neighbor search under elastic distances is a key tool for time series analysis, supporting many applications. However, straightforward implementations of distances require $O(n^2)$ space and time complexities, preventing these applications from scaling to long series. Much work has been devoted to speeding up the NN search process, mostly with the development of lower bounds, allowing to avoid costly distance computations when a given threshold is exceeded. This threshold, provided by the similarity search process, also allows to early abandon the computation of a distance itself. Another approach, is to prune parts of the computation. All these techniques are othogonal to each other. In this work, we develop a new generic strategy, "EAPruned", that tightly integrates pruning with early abandoning. We apply it to six elastic distance measures: DTW, CDTW, WDTW, ERP, MSM and TWE, showing substantial speedup in NN search applications. Pruning alone also shows substantial speedup for some distances, benefiting applications beyond the scope of NN search (e.g. requiring all pairwise distances), and hence where early abandoning is not applicable. We~release our implementation as part of a new C++ library for time series classification, along with easy to use Python/Numpy bindings.