Unified Modeling and Clustering of Mobility Trajectories with Spatiotemporal Point Processes

In various application domains like transportation, urban planning, and public health, analyzing human mobility, represented as a sequence of consecutive visits (aka trajectories), is crucial for uncovering essential mobility patterns. Current practices often discretize space and time to model trajectory data with sequence-analysis techniques like Transformers and LSTM, but this discretization tends to obscure the intrinsic spatial and temporal characteristics inherent in trajectories. Recent work shows the effectiveness of modeling trajectories directly in continuous space and time using the spatiotemporal point process (STPP). However, these approaches often assume that all observed trajectories originate from a single underlying dynamic. In reality, real-world trajectories exhibit varying dynamics or moving patterns. We hypothesize that grouping trajectories governed by similar dynamics into clusters before trajectory modeling could enhance modeling effectiveness. Thus, we present a novel approach that simultaneously models trajectories in continuous space and time using STPP while clustering them. Our method leverages a variational Expectation-Maximization (EM) framework to iteratively improve the learning of trajectory dynamics and refine cluster assignments within a single training phase. Extensive tests on synthetic and real-world data demonstrate its effectiveness in clustering and modeling trajectories.