Deep trajectory modeling has garnered significant attention across various applications, particularly in trajectory user linking (TUL), which aims to associate trajectories with specific users by analyzing complex mobility patterns. Despite its advancements, the lack of explainability remains a critical challenge. In this article, we propose a general Information Bottleneck framework, TUL-IB, designed to enhance the explainability of TUL models for both sequence and graph data, with tractable optimization bounds to solve the TUL-IB objective. We further demonstrate that TUL-IB can be effectively applied to two distinct types of trajectory data: (1) waypoint trajectories, for which we extend TUL-IB into a dual-view approach, TUL-DV-IB, integrating both driving behavior sequences and trajectory road graphs. To ensure temporal continuity in subsequence selection, we employ dynamic programming during post-processing; (2) staypoint trajectories, for which we adapt TUL-IB to the graph node level and apply it to global trajectory graph model, resulting in TUL-GTG-IB. This adaptation identifies key neighboring trajectories that significantly contribute to explaining the user-linking results. Experimental results on three real-world datasets demonstrate that our method outperforms existing explainable approaches, providing deeper insights into trajectory user-linking models.

Trajectory anomaly detection is critical in trajectory data mining. The objective is to identify abnormal movements of objects. Most existing trajectory anomaly detection methods focus on determining whether an entire trajectory is anomalous, lacking the ability to identify the exact anomalous sub-trajectories. Although recent research has started addressing anomalous sub-trajectories detection, these methods fail to extract the specific route pattern for the target trajectory. As a result, they struggle to identify anomalous sub-trajectories when the same sub-trajectory is regarded as normal in other routes. To overcome these limitations, we propose a Route-Enhanced Conditional Anomalous Sub-Trajectory detection model (RECAST). RECAST has two innovative components: (1) a Route Discovery Network (RDN) that extracts the normal route pattern of the given trajectory; (2) a Conditional Anomalous Sub-trajectory Detection (CASD) network that detects anomalies conditioned on the estimated route patterns. Our design enables RECAST to identify sub-trajectories as anomalous even if they are normal in other routes, as long as they are unlikely to occur in the route of the given trajectory. We evaluate the effectiveness and efficiency of RECAST using two real-world datasets. The results demonstrate that our method outperforms the state-of-the-art methods in detection accuracy with competitive runtime efficiency1.

This work addresses a key limitation in current federated learning approaches, which predominantly focus on homogeneous tasks, neglecting the task diversity on local devices. We propose a principled integration of multi-task learning using multi-output Gaussian processes (MOGP) at the local level and federated learning at the global level. MOGP handles correlated classification and regression tasks, offering a Bayesian non-parametric approach that naturally quantifies uncertainty. The central server aggregates the posteriors from local devices, updating a global MOGP prior redistributed for training local models until convergence. Challenges in performing posterior inference on local devices are addressed through the Polya-Gamma augmentation technique and mean-field variational inference, enhancing computational efficiency and convergence rate. Experimental results on both synthetic and real data demonstrate superior predictive performance, OOD detection, uncertainty calibration and convergence rate, highlighting the method's potential in diverse applications. Our code is publicly available at https://github.com/JunliangLv/task_diversity_BFL.