The elasticity of the DTW metric provides a more flexible comparison between time series and is used in numerous machine learning domains such as classification or clustering. However, it does not align the measurements at the beginning and end of time series if they have a shift occurring right at the start of one series, with the omitted part appearing at the end of that series. Due to the cyclicity of such series - which lack a definite beginning or end - we rely on the Cyclic DTW approach to propose a less computationally expensive approximation of this calculation method. This approximation will then be employed in conjunction with the K-Means clustering method.

翻译：DTW度量的弹性为时间序列提供了更灵活的比较方式，并被广泛应用于分类、聚类等机器学习领域。然而，若某一时间序列的开头存在偏移现象（即该序列起始处缺失的部分出现在其结尾处），标准的DTW度量无法对齐该序列起始与结尾处的测量值。鉴于此类循环序列缺乏明确的起始或终点，我们基于循环DTW方法提出了一种计算成本更低的近似算法。该近似方法随后将与K-Means聚类方法结合使用。