# Making the Dynamic Time Warping Distance Warping-Invariant

## TL;DR

This paper introduces a new warping-invariant semi-metric called the twi-distance, addressing the non-invariance of DTW, leading to more efficient and consistent time series classification.

## Contribution

The paper proposes the twi-distance, a warping-invariant semi-metric, improving consistency and efficiency over the traditional DTW distance in time series analysis.

## Key findings

- Twi-distance is practically equivalent to DTW in classification error rates.
- Twi-distance requires less storage and computation time than DTW.
- The results challenge the common use of DTW in nearest-neighbor classification.

## Abstract

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.