Similarity measure of time series based on Angle-distance Penalized Metric Dynamic Time Warping

Measuring the similarity of time series is a fundamental task in numerous information processing applications. Dynamic Time Warping (DTW) is a widely used method for time series similarity measurement, yet its reliance solely on linear Euclidean distance and neglect of directional information often limits its ability in scenarios where subtle variations and trajectory orientation carry semantic significance. To address these limitations, we propose Angle-distance Penalized Metric DTW (APMDTW), a novel similarity measure method that integrates a nonlinear spatial distance metric with an adaptive angle-distance penalty. Specifically, a piecewise logarithmic transformation is introduced to enhance sensitivity to fine-grained local differences, while a parameterized angle-distance penalty, adaptively modulated by spatial distance, incorporates directional consistency into the cost function. This joint modeling of spatial magnitude and geometric orientation yields a more discriminative and robust time series similarity measurement. Experiments on 128 UCR benchmark datasets show that APMDTW outperforms six baseline algorithms on 114 datasets, and improves similarity measurement accuracy by an average of 56.52% over six state-of-the-art DTW variants.