Discovering time series motifs of all lengths using dynamic time warping

Motif discovery is a fundamental operation in the analysis of time series data. Existing motif discovery algorithms that support Dynamic Time Warping require manual determination of the exact length of motifs. However, setting appropriate length for interesting motifs can be challenging and selecting inappropriate motif lengths may result in valuable patterns being overlooked. This paper addresses the above problem by proposing algorithms that automatically compute motifs of all lengths using Dynamic Time Warping. Specifically, a batch algorithm as well as an anytime algorithm are designed in this paper, which are refered as BatchMotif and AnytimeMotif respectively. The proposed algorithms achieve significant improvements in efficiency by fully leveraging the correlations between the motifs of different lengths. Experiments conducted on real datasets demonstrate the superiority of both of the proposed algorithms. On average, BatchMotif is 13 times faster than the baseline method. Additionally, AnytimeMotif is 7 times faster than the baseline method and is capable of providing relatively satisfying results with only a small portion of calculation.