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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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As the availability and use of wearables increases, they are becoming a promising platform for context sensing and context analysis. Smartwatches are a particularly interesting platform for this purpose, as they offer salient advantages, such as their proximity to the human body. However, they also have limitations associated with their small form factor, such as processing power and battery life, which makes it difficult to simply transfer smartphone-based context sensing and prediction models to smartwatches. In this paper, we introduce an energy-efficient, generic, integrated framework for continuous context sensing and prediction on smartwatches. Our work extends previous approaches for context sensing and prediction on wrist-mounted wearables that perform predictive analytics outside the device. We offer a generic sensing module and a novel energy-efficient, on-device prediction module that is based on a semantic abstraction approach to convert sensor data into meaningful information objects, similar to human perception of a behavior. Through six evaluations, we analyze the energy efficiency of our framework modules, identify the optimal file structure for data access and demonstrate an increase in accuracy of prediction through our semantic abstraction method. The proposed framework is hardware independent and can serve as a reference model for implementing context sensing and prediction on small wearable devices beyond smartwatches, such as body-mounted cameras.