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Clustering time series is a useful operation in its own right, and an important subroutine in many higher-level data mining analyses, including data editing for classifiers, summarization, and outlier detection. While it has been noted that the general superiority of Dynamic Time Warping (DTW) over Euclidean Distance for similarity search diminishes as we consider ever larger datasets, as we shall show, the same is not true for clustering. Thus, clustering time series under DTW remains a computationally challenging task. In this work, we address this lethargy in two ways. We propose a novel pruning strategy that exploits both upper and lower bounds to prune off a large fraction of the expensive distance calculations. This pruning strategy is admissible; giving us provably identical results to the brute force algorithm, but is at least an order of magnitude faster. For datasets where even this level of speedup is inadequate, we show that we can use a simple heuristic to order the unavoidable calculations in a most-useful-first ordering, thus casting the clustering as an anytime algorithm. We demonstrate the utility of our ideas with both single and multidimensional case studies in the domains of astronomy, speech physiology, medicine and entomology.

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The detection of time series motifs, which are approximately repeated subsequences in time series streams, has been shown to have great utility as a subroutine in many higher-level data mining algorithms. However, this detection becomes much harder in cases where the motifs of interest are vanishingly rare or when faced with a never-ending stream of data. In this work we investigate algorithms to find such rare motifs. We demonstrate that under reasonable assumptions we must abandon any hope of an exact solution to the motif problem as it is normally defined; however, we introduce algorithms that allow us to solve the underlying problem with high probability.

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