Time series classification and clustering are important for data mining research, which is conducive to recognizing movement patterns, finding customary routes, and detecting abnormal trajectories in transport (e.g. road and maritime) traffic. The dynamic time warping (DTW) algorithm is a classical distance measurement method for time series analysis. However, the over-stretching and over-compression problems are typical drawbacks of using DTW to measure distances. To address these drawbacks, an adaptive constrained DTW (ACDTW) algorithm is developed to calculate the distances between trajectories more accurately by introducing new adaptive penalty functions. Two different penalties are proposed to effectively and automatically adapt to the situations in which multiple points in one time series correspond to a single point in another time series. The novel ACDTW algorithm can adaptively adjust the correspondence between two trajectories and obtain greater accuracy between different trajectories. Numerous experiments on classification and clustering are undertaken using the UCR time series archive and real vessel trajectories. The classification results demonstrate that the ACDTW algorithm performs better than four state-of-the-art algorithms on the UCR time series archive. Furthermore, the clustering results reveal that the ACDTW algorithm has the best performance among three existing algorithms in modeling maritime traffic vessel trajectory.

时间序列分类和聚类对于数据挖掘研究非常重要，这有助于识别运动模式，查找惯用路线以及检测运输（例如公路和海上）交通中的异常轨迹。动态时间规整（DTW）算法是用于时间序列分析的经典距离测量方法。但是，过度拉伸和过度压缩问题是使用DTW测量距离的典型缺点。为了解决这些缺点，开发了一种自适应约束DTW（ACDTW）算法，以通过引入新的自适应惩罚函数来更准确地计算轨迹之间的距离。为了有效和自动地适应一个时间序列中的多个点对应于另一个时间序列中的单个点的情况，提出了两种不同的惩罚措施。新颖的ACDTW算法可以自适应地调整两个轨迹之间的对应关系，并在不同轨迹之间获得更高的精度。使用UCR时间序列档案和实际船只轨迹进行了许多有关分类和聚类的实验。分类结果表明，在UCR时间序列档案库中，ACDTW算法的性能优于四种最新算法。此外，聚类结果表明，在海上交通船舶航迹建模中，ACDTW算法在三种现有算法中表现最佳。使用UCR时间序列档案和实际船只轨迹进行了许多有关分类和聚类的实验。分类结果表明，在UCR时间序列档案库中，ACDTW算法的性能优于四种最新算法。此外，聚类结果表明，在海上交通船舶航迹建模中，ACDTW算法在三种现有算法中表现最佳。使用UCR时间序列档案和实际船只轨迹进行了许多有关分类和聚类的实验。分类结果表明，在UCR时间序列档案库中，ACDTW算法的性能优于四种最新算法。此外，聚类结果表明，在海上交通船舶航迹建模中，ACDTW算法在三种现有算法中表现最佳。