Ultra fast warping window optimization for Dynamic Time Warping

The Dynamic Time Warping (DTW) similarity measure is widely used in many time series data mining applications. It computes the cost of aligning two series, smaller costs indicating more similar series. Most applications require tuning of DTW's Warping Window (WW) parameter in order to achieve good performance. This parameter controls the amount of warping allowed, reducing pathological alignments, with the added benefit of speeding up computation. However, since DTW is in itself very costly, learning the WW is a burdensome process, requiring days even for datasets containing only a few thousand series. In this paper, we propose ULTRAFASTWWSEARCH, a new algorithm able to learn the WW significantly faster than the state-of-the-art FAsTWWSEARCH method. ULTRAFASTWWSEARCH builds upon the latter, exploiting the properties of a new efficient exact DTW algorithm which supports early abandoning and pruning (EAP). We show on 128 datasets from the UCR archive that ULTRAFASTWWSEARCH is up to an order of magnitude faster than the previous state of the art.