Multivariate Spatio-Temporal Neural Hawkes Processes

We propose a Multivariate Spatio-Temporal Neural Hawkes Process for modeling complex multivariate event data with spatio-temporal dynamics. The proposed model extends continuous-time neural Hawkes processes by integrating spatial information into latent state evolution through learned temporal and spatial decay dynamics, enabling flexible modeling of excitation and inhibition without predefined triggering kernels. By analyzing fitted intensity functions of deep learning-based temporal Hawkes process models, we identify a modeling gap in how fitted intensity behavior is captured beyond likelihood-based performance, which motivates the proposed spatio-temporal approach. Simulation studies show that the proposed method successfully recovers sensible temporal and spatial intensity structure in multivariate spatio-temporal point patterns, while existing temporal neural Hawkes process approach fails to do so. An application to terrorism data from Pakistan further demonstrates the proposed model's ability to capture complex spatio-temporal interaction across multiple event types.

A Spatio-temporal Track Association Algorithm Based on Marine Vessel Automatic Identification System Data

Tracking multiple moving objects in real-time in a dynamic threat environment is an important element in national security and surveillance system. It helps pinpoint and distinguish potential candidates posing threats from other normal objects and monitor the anomalous trajectories until intervention. To locate the anomalous pattern of movements, one needs to have an accurate data association algorithm that can associate the sequential observations of locations and motion with the underlying moving objects, and therefore, build the trajectories of the objects as the objects are moving. In this work, we develop a spatio-temporal approach for tracking maritime vessels as the vessel's location and motion observations are collected by an Automatic Identification System. The proposed approach is developed as an effort to address a data association challenge in which the number of vessels as well as the vessel identification are purposely withheld and time gaps are created in the datasets to mimic the real-life operational complexities under a threat environment. Three training datasets and five test sets are provided in the challenge and a set of quantitative performance metrics is devised by the data challenge organizer for evaluating and comparing resulting methods developed by participants. When our proposed track association algorithm is applied to the five test sets, the algorithm scores a very competitive performance.