ABSTRACT

The study of trajectories of people, vehicles, and animals has many applications. Clustering is one of the ways to extract movement behaviors in trajectories. Due to the complex behavioral nature of trajectories, different geometric criteria, such as distance, shape, sinuosity, complexity, and orientation, are used for trajectory (dis)similarity calculation depending on the types of data. Comparison of trajectories based on shape is one of the approaches used to measure the similarity of trajectories for clustering. Up to now, different functions and descriptors have been proposed to compare two trajectories based on shape. However, the efficiency of these functions and descriptors in trajectory clustering has not been evaluated. In this paper, the similarity of trajectories based on shape was evaluated for trajectories clustering. Turning, signature, tangent, radius vector functions, and shape context descriptors are used for this evaluation. In addition, shape similarity of trajectories from the perspective of curvature, sinuosity, and complexity is also assessed. Since the criteria utilized are not the distance, clustering of trajectories has some limitations compared to previous clustering algorithms. To overcome these limitations, a framework called Clustering based on Representative Trajectories of Dense Areas (CRTDA) has been proposed for automatic clustering of trajectories. This framework can also be used for points and trajectories clustering based on other geometric criteria such as distance. Evaluations were performed on one simulated dataset and three real datasets, including pedestrian, car, and aircraft tracks. Finally, a practical comparison was made in terms of the diversity and quality of valid clusters and execution time between different criteria. According to the results, in terms of the variety and the number of clusters, the turning function and shape context with the mean of seven and four clusters provide a better performance, respectively. In terms of the clustering quality, the shape context and radius vector functions with mean silhouette index of 0.626 and 0.477, respectively, provide better performance. Moreover, signature and MA-sinuosity functions, respectively, with 43.2 and 49.5 seconds on average, provide better performance in terms of the execution time.

摘要

对人、车辆和动物轨迹的研究有很多应用。聚类是提取轨迹中运动行为的方法之一。由于轨迹的复杂行为性质，不同的几何标准，如距离、形状、曲折度、复杂性和方向，用于根据数据类型进行轨迹（非）相似性计算。基于形状的轨迹比较是用于测量聚类轨迹相似性的方法之一。到目前为止，已经提出了不同的函数和描述符来比较基于形状的两条轨迹。然而，这些函数和描述符在轨迹聚类中的效率尚未得到评估。在本文中，基于形状的轨迹相似性被评估用于轨迹聚类。转身，签名、切线、半径矢量函数和形状上下文描述符用于此评估。此外，还从曲率、曲率和复杂性的角度评估了轨迹的形状相似性。由于使用的标准不是距离，因此与以前的聚类算法相比，轨迹聚类具有一些局限性。为了克服这些限制，已经提出了一种称为基于密集区域代表性轨迹（CRTDA）的聚类的框架，用于轨迹的自动聚类。该框架还可用于基于其他几何标准（例如距离）的点和轨迹聚类。对一个模拟数据集和三个真实数据集进行了评估，包括行人、汽车和飞机轨迹。最后，在有效集群的多样性和质量以及不同标准之间的执行时间方面进行了实际比较。根据结果​​，在簇的种类和数量方面，具有七个和四个簇的均值的转向函数和形状上下文分别提供了更好的性能。在聚类质量方面，平均轮廓指数分别为 0.626 和 0.477 的形状上下文和半径向量函数提供了更好的性能。此外，签名和 MA-sinuosity 函数分别平均为 43.2 和 49.5 秒，在执行时间方面提供了更好的性能。具有七个和四个集群平均值的转向函数和形状上下文分别提供了更好的性能。在聚类质量方面，平均轮廓指数分别为 0.626 和 0.477 的形状上下文和半径向量函数提供了更好的性能。此外，签名和 MA-sinuosity 函数分别平均为 43.2 和 49.5 秒，在执行时间方面提供了更好的性能。具有七个和四个集群平均值的转向函数和形状上下文分别提供了更好的性能。在聚类质量方面，平均轮廓指数分别为 0.626 和 0.477 的形状上下文和半径向量函数提供了更好的性能。此外，签名和 MA-sinuosity 函数分别平均为 43.2 和 49.5 秒，在执行时间方面提供了更好的性能。