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

TL;DR

This paper introduces the first scalable exact algorithm for discovering time series motifs using Dynamic Time Warping (DTW), significantly reducing computation through a hierarchy of lower bounds.

Contribution

It presents a novel hierarchical lower bounds framework that enables efficient exact motif discovery under DTW, overcoming previous computational challenges.

Findings

Prunes up to 99.99% of DTW calculations in realistic settings

Achieves a superior trade-off between computation time and accuracy

First exact method for DTW-based motif discovery

Abstract

Over the last decade, time series motif discovery has emerged as a useful primitive 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) is the best time series similarity measure in a host of settings. Surprisingly however, there has been virtually no work on using DTW to discover motifs. The most obvious explanation of this is the fact that both motif discovery and the use of DTW can be computationally challenging, and the current best mechanisms to address their lethargy are mutually incompatible. In this work, we present the first scalable exact method to discover time series motifs under DTW. Our method automatically performs the best trade-off between time-to-compute and tightness-of-lower-bounds for a novel hierarchy of lower bounds representation we introduce. We show that under realistic settings, our algorithm can admissibly prune up to 99.99% of the DTW computations.