A novel approach for cluster detection in trajectory data with low cluster-to-noise density ratio

A spatial cluster of trajectories refers to objects that follow similar paths, revealing shared movement trends and aiding in anomaly detection. However, detecting clusters in trajectory data becomes challenging when the cluster-to-noise density ratio (CNDR) is low. For example, clusters in free-range sheep movements are easily seen due to their group behaviour, whereas the diversity of human movement introduces significant noise, making clustering difficult. The L-function, widely used for clustering detection in various data types (e.g. point or OD flow data), captures aggregation changes across scales without relying on predefined thresholds, offering potential for low CNDR trajectory data. Thus, we define a trajectory space to derive the Trajectory L (TL)-function for multipoint trajectories. Then we use the second derivative of the TL-function and the local TL-function to identify cluster sizes and extract clusters. Inflection points in the second derivatives enable the detection of subtle changes in aggregation, allowing for precise and sensitive cluster identification. Simulation experiments show that our method outperforms four state-of-the-art approaches in detecting clusters under low CNDR conditions while avoiding parameter dependency. We validated the generality and robustness of our method using both taxi GPS trajectories and mobile phone signalling trajectories. Furthermore, our work lays a rigorous and extensible foundation for the future formulation of spatiotemporal statistical frameworks tailored to trajectory data.