Time series motifs discovery under DTW allows more robust discovery of conserved structure

Abstract

In recent years, time series motif discovery has emerged as perhaps the most important primitive for many analytical tasks, including clustering, classification, rule discovery, segmentation, and summarization. In parallel, it has long been known that Dynamic Time Warping (DTW) is superior to other similarity measures such as Euclidean Distance under most settings. However, due to the computational complexity of both DTW and motif discovery, virtually no research efforts have been directed at combining these two ideas. The current best mechanisms to address their lethargy appear to be mutually incompatible. In this work, we present the first efficient, scalable and exact method to find time series motifs under DTW. Our method automatically performs the best trade-off of time-to-compute versus tightness-of-lower-bounds for a novel hierarchy of lower bounds that we introduce. As we shall show through extensive experiments, our algorithm prunes up to 99.99% of the DTW computations under realistic settings and is up to three to four orders of magnitude faster than the brute force search, and two orders of magnitude faster than the only other competitor algorithm. This allows us to discover DTW motifs in massive datasets for the first time. As we will show, in many domains, DTW-based motifs represent semantically meaningful conserved behavior that would escape our attention using all existing Euclidean distance-based methods.