Exact Discovery of Time Series Motifs

Time series motifs are pairs of individual time series, or subsequences of a longer time series, which are very similar to each other. As with their discrete analogues in computational biology, this similarity hints at structure which has been conserved for some reason and may therefore be of interest. Since the formalism of time series motifs in 2002, dozens of researchers have used them for diverse applications in many different domains. Because the obvious algorithm for computing motifs is quadratic in the number of items, more than a dozen approximate algorithms to discover motifs have been proposed in the literature. In this work, for the first time, we show a tractable exact algorithm to find time series motifs. As we shall show through extensive experiments, our algorithm is up to three orders of magnitude faster than brute-force search in large datasets. We further show that our algorithm is fast enough to be used as a subroutine in higher level data mining algorithms for anytime classification, near-duplicate detection and summarization, and we consider detailed case studies in domains as diverse as electroencephalograph interpretation and entomological telemetry data mining.