Semi-Metrification of the Dynamic Time Warping Distance
This addresses peculiarities in data mining applications for time series analysis, but it is incremental as it builds on existing DTW methods without major breakthroughs.
The paper tackled the problem that the dynamic time warping (DTW) distance lacks metric properties like the triangle inequality, leading to issues in data mining. They converted DTW to a semi-metric, showing its canonical extension is warping-invariant, and found that a nearest-neighbor classifier in this space performs comparably to one in standard DTW-space.
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.