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. In this work, for the first time, we show a tractable exact algorithm to find time series motifs. While our exact algorithm is still worst case quadratic, we show that we can reduce the time required by three orders of magnitude. In fact, under most realistic conditions our exact algorithm is faster than the current linear time approximate algorithms, because they have such large constant factors. As we shall show, our algorithm allows us to tackle problems which have previously been thought intractable, for example automatically constructing "dictionaries" of recurring patterns from electroencephalographs. We further show that our algorithm is fast enough to be used as a subroutine in higher level data mining algorithms for summarization, near-duplicate detection and anytime classification [34] . KEYWORDS
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Exact Discovery of Time Series Motifs
SDM
Medicine Computer Science