# Making the Dynamic Time Warping Distance Warping-Invariant

arXiv: https://arxiv.org/abs/1903.01454 · HTML: https://mlsanity.com/paper/1903.01454/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2019.

## Built on by (most cited first, 2 of 2)

- [FRUITS: Feature Extraction Using Iterated Sums for Time Series Classification](https://mlsanity.com/paper/2311.14549/) (2023)
- [Accurate shape and phase averaging of time series through Dynamic Time Warping](https://mlsanity.com/paper/2109.00978/) (2021)

## Abstract (arXiv)

The literature postulates that the dynamic time warping (dtw) distance can cope with temporal variations but stores and processes time series in a form as if the dtw-distance cannot cope with such variations. To address this inconsistency, we first show that the dtw-distance is not warping-invariant. The lack of warping-invariance contributes to the inconsistency mentioned above and to a strange behavior. To eliminate these peculiarities, we convert the dtw-distance to a warping-invariant semi-metric, called time-warp-invariant (twi) distance. Empirical results suggest that the error rates of the twi and dtw nearest-neighbor classifier are practically equivalent in a Bayesian sense. However, the twi-distance requires less storage and computation time than the dtw-distance for a broad range of problems. These results challenge the current practice of applying the dtw-distance in nearest-neighbor classification and suggest the proposed twi-distance as a more efficient and consistent option.