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Measuring distance or similarity between time-series data is a fundamentalaspect of many applications including classification, clustering, andensembling/alignment. Existing measures may fail to capture similarities amonglocal trends (shapes) and may even produce misleading results. Our goal is todevelop a measure that looks for similar trends occurring around similar timesand is easily interpretable for researchers in applied domains. This isparticularly useful for applications where time-series have a sequence ofmeaningful local trends that are ordered, such as in epidemics (a surge to anincrease to a peak to a decrease). We propose a novel measure, DTW+S, whichcreates an interpretable "closeness-preserving" matrix representation of thetime-series, where each column represents local trends, and then it appliesDynamic Time Warping to compute distances between these matrices. We present atheoretical analysis that supports the choice of this representation. Wedemonstrate the utility of DTW+S in several tasks. For the clustering ofepidemic curves, we show that DTW+S is the only measure able to produce goodclustering compared to the baselines. For ensemble building, we propose acombination of DTW+S and barycenter averaging that results in the bestpreservation of characteristics of the underlying trajectories. We alsodemonstrate that our approach results in better classification compared toDynamic Time Warping for a class of datasets, particularly when local trendsrather than scale play a decisive role.

DTW+S: Shape-based Comparison of Time-series with Ordered Local Trend