Optimal Warping Paths are unique for almost every pair of Time Series
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An optimal warping path between two time series is generally not unique. The size and form of the set of pairs of time series with non-unique optimal warping path is unknown. This article shows that optimal warping paths are unique for almost every pair of time series in a measure-theoretic sense. All pairs of time series with non-unique optimal warping path form a negligible set and are geometrically the union of zero sets of quadratic forms. The result is useful for analyzing and understanding adaptive learning methods in dynamic time warping spaces.
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