Semi-Metrification of the Dynamic Time Warping Distance

TL;DR

This paper introduces a semi-metric version of the dynamic time warping distance to address its mathematical shortcomings, maintaining classification performance while improving data mining robustness.

Contribution

It converts DTW into a semi-metric, ensuring warping-invariance and better mathematical properties without sacrificing classifier accuracy.

Findings

Semi-metric DTW performs comparably to standard DTW in classification tasks.

Canonical extension of semi-metric DTW is warping-invariant.

Proposes a new mathematical framework for DTW in data mining.

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.