G‐<scp>WVDTW</scp>: A <scp>Generalised Weighted</scp> Variance Dynamic Time Warping Algorithm for Subsequence Matching in Multivariate Time Series

ABSTRACT Dynamic time warping (DTW) is an algorithm used to measure the similarity between sequences, with widespread applications in domains such as speech recognition, image processing and video synchronisation. However, when matching a shorter multivariate time subsequence to a longer time series containing a similar subsequence, existing DTW variants struggle to accurately determine the matching path. To address this issue, we propose an improved algorithm, generalised weighted variance DTW (G‐WVDTW). We extend the DTW algorithm to multivariate time series and introduce a weighted variance‐based approach to calculate local distances. This allows the algorithm to better assess the distance between different time points in multivariate time series. Additionally, we modify the algorithm's boundary conditions, enabling it to handle subsequence matching tasks in multivariate time series. We conducted similarity retrieval experiments using public datasets and evaluated the algorithm's performance with the AUC metric, achieving up to a 19% improvement on certain datasets. Furthermore, we performed alignment experiments on industrial data, where we artificially generated aligned sequences and quantitatively assessed the alignment errors, which were lower than those produced by other DTW variants. Finally, we validated the algorithm's superior performance in multivariate time series subsequence matching tasks using a synthetic dataset and showcased its use in motif detection using a wind power generation dataset. The algorithm can be applied in fields such as industrial, meteorological and electrocardiogram (ECG) signal analysis for tasks like time series retrieval, matching and data labelling.