An accurate slicing method for dynamic time warping algorithm and the segment-level early abandoning optimization

Time series data analysis algorithms have been gaining significant importance in the research community. Extensive studies have confirmed that Dynamic Time Warping (DTW) is the best distance measure in time series analysis across multiple domains. However, DTW is a time-consuming algorithm with quadratic time complexity, which limits its widespread adoption. In this paper, we proposed a novel slicing mechanism for DTW, called Partial Dynamic Time Warping (PDTW). PDTW is capable of dividing a complete DTW calculation into multiple independent partial calculations. The proposed PDTW ensures very consistent alignments with the original Constrained DTW (CDTW) by incorporating additional data windows for each pairwise time series. On the basis of PDTW, we also present Early Abandoning Dynamic Time Warping (EADTW) technique, which saves a substantial amount of computing time by abandoning superfluous calculations of unnecessary segments in the time series classification task. Large-scale experimental results on 96 datasets from the UCR archive show the effectiveness of PDTW and EADTW. The cumulative sum of PDTW distances for segments is nearly identical to the CDTW distance, and in many cases, it is exactly equal. This remarkable characteristic of PDTW indicates its immense potential for further development and optimization of DTW, such as parallelization. In classification tasks, EADTW is 1.99 times faster than CDTW on average, with a maximum speedup of 2.89 times, while maintaining accuracy. Additionally, it enhances accuracy by 0.93% and improves speed by 2.34 times under the accuracy priority parameter.