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Over the last decade, time series motif discovery has emerged as a usefulprimitive for many downstream analytical tasks, including clustering,classification, rule discovery, segmentation, and summarization. In parallel,there has been an increased understanding that Dynamic Time Warping (DTW) isthe best time series similarity measure in a host of settings. Surprisinglyhowever, there has been virtually no work on using DTW to discover motifs. Themost obvious explanation of this is the fact that both motif discovery and theuse of DTW can be computationally challenging, and the current best mechanismsto address their lethargy are mutually incompatible. In this work, we presentthe first scalable exact method to discover time series motifs under DTW. Ourmethod automatically performs the best trade-off between time-to-compute andtightness-of-lower-bounds for a novel hierarchy of lower bounds representationwe introduce. We show that under realistic settings, our algorithm canadmissibly prune up to 99.99% of the DTW computations.

Matrix Profile XXII: Exact Discovery of Time Series Motifs under DTW