AdaPDTW: An Efficient Abstract-Adaptive Piecewise Dynamic Time Warping for Time Series Classification

Dynamic Time Warping (DTW) offers precise similarity measure but suffers from high computational cost. To address this issue, we propose an abstract-adaptive PAR-DTW, which computes DTW in a low-dimensional piecewise abstract representation (PAR) space. Unlike existing methods that use globally uniform pointwise measures, our approach clusters abstracts and learns adaptive pointwise measures for each cluster pair. We formulate a joint objective function that combines global classification loss with local clustering loss, and introduce an efficient optimization method based on closed-form solutions. This enhances local adaptability while significantly reducing computational complexity. Experimental results demonstrate that our method achieves precision comparable to DTW and significantly outperforms existing PAR-DTW methods, offering up to four orders of magnitude in speedup.