Semi-Metrification of the Dynamic Time Warping Distance

Abstract

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.

References in corpus (2)

• Time Warp Edit Distance with Stiffness Adjustment for Time Series Matching
• On the Existence of a Sample Mean in Dynamic Time Warping Spaces

Cited by in corpus (1)

• Diffeomorphic Transformations for Time Series Analysis: An Efficient Approach to Nonlinear Warping