Making the Dynamic Time Warping Distance Warping-Invariant
This addresses an inconsistency in time series analysis for researchers and practitioners, offering a more efficient alternative to DTW, though it is incremental as it modifies an existing method.
The paper tackled the inconsistency that the dynamic time warping (DTW) distance is not warping-invariant, which leads to inefficiencies, and proposed a warping-invariant semi-metric called time-warp-invariant (TWI) distance. The result shows that TWI and DTW have practically equivalent error rates in nearest-neighbor classification, but TWI requires less storage and computation time for many problems.
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.