Effective and robust clustering for spatiotemporally dependent data

Spatio-temporal data exists in various fields such as transportation and environment, and the analysis of clustering plays a critical role in understanding such data. However, spatio-temporal clustering faces challenges, as it is frequently affected by the time length of data and the intricate dependence structure of spatio-temporal data. In this work, we propose a robust approach to achieve the fuzzy clustering of complex spatio-temporal data. This involves two key technologies: (1) the reconstruction of spatio-temporal data using B-splines, and (2) the incorporation of a weighted exponential function to characterize spatial and temporal dependencies. The data reconstruction reduces the impact of the time length on clustering while improving computational efficiency. Meanwhile, the integration of a spatio-temporal scaling factor within the weighted function addresses the scale difference between spatial and temporal coordinates. For the implementation, the clustering process is performed using the Partitioning Around Medoids (PAM) algorithm, and the optimization of the number of clusters is achieved through the use of the fuzzy silhouette coefficient. Extensive simulation studies and two real-world applications are used to demonstrate the effectiveness of the proposed method.