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Semi-Metrification of the Dynamic Time Warping Distance

by   Brijnesh J. Jain, et al.

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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