Semi-Metrification of the Dynamic Time Warping Distance
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The dynamic time warping (dtw) distance fails to satisfy the triangle inequality and the identity of indiscernibles. As a consequence, the dtw-distance is not warping-invariant, which in turn results in peculiarities in data mining applications. This article converts the dtw-distance to a semi-metric and shows that its canonical extension is warping-invariant. Empirical results indicate that the nearest-neighbor classifier in the proposed semi-metric space performs comparable to the same classifier in the standard dtw-space. To overcome the undesirable peculiarities of dtw-spaces, this result suggest to further explore the semi-metric space for data mining applications.
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