Making the dynamic time warping distance warping-invariant

•The dtw-distance is not warping-invariant.•Lack of warping-invariance contributes to inconsistencies and peculiarities.•Converts dtw-distance into a warping-invariant semi-metric.•Proposed semi-metric is more efficient than dtw-distance.•Error-rates of nn-classifiers in semi-metric and dtw-space are practically equivalent.