Efficient Discovery of Time Series Motifs under both Length Differences and Warping

Over the past two decades, time series motif discovery has become a crucial subroutine for many time series data mining tasks; concurrently, it has been established that Dynamic Time Warping (DTW) outperforms other similarity measures like Euclidean Distance in most scenarios. Against this backdrop, a DTW motif discovery algorithm was recently developed; however, it is confined to working with fixed-length subsequences. In this work, we propose a novel approach that allows us to find motifs under both length differences and warping. Our algorithm exploits a promising time series representation called Spikelets and introduces the first lower bound for DTW in the Spikelet space. Extensive empirical studies demonstrate that our method scales effectively across various real-world datasets and efficiently identifies DTW motif pairs of different lengths.