  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 comparably to the same classifier in the standard
dtw-space. To overcome the undesirable peculiarities of dtw-spaces, this result
suggests to further explore the semi-metric space for data mining applications.
