An assessment on the performance of the shape functions in clustering based on representative trajectories of dense areas

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.