HybridFTW: Hybrid Computation of Dynamic Time Warping Distances

In this paper, we propose an efficient approach that computes the dynamic time warping (DTW) distance in time-series similarity search. The DTW distance is known to offer the high accuracy in similarity search, but it has difficulty in supporting the large database due to its high computational complexity. Recently, FastDTW and FTW have been proposed for efficient computation of DTW distances, but they have still performance limitations. In this paper, we propose a hybrid approach, called HybridFTW, which combines the advantages of both FastDTW and FTW. First, HybridFTW takes the advantage of FastDTW that provides fast computation through the limitation of allowable ranges. We call these allowable ranges dynamic (warping) bands, which reduce the computation spaces on the fly, and we reanalyze previous FastDTW and FTW in the viewpoint of static and dynamic bands. Second, HybridFTW also takes the advantage of FTW that exploits the early abandon effect by using the segment-based tight lower bound. To maximize the synergy of combining two methods, we obtain the dynamic band of FastDTW during the process of computing the lower bound in FTW. Using HybridFTW, we next propose range search and k-NN search algorithms and prove their correctness through formal theorems. Experimental results on real and synthetic data sets show that HybridFTW improves the search performance by up to 38 times over FastDTW and by up to 12 times over FTW.