Hyperspectral Trajectory Image for Multi-Month Trajectory Anomaly Detection

Abstract: Trajectory anomaly detection underpins applications from fraud detection to urban mobility analysis. Dense GPS methods preserve fine-grained evidence such as abnormal speeds and short-duration events, but their quadratic cost makes multi-month analysis intractable; consequently, no existing approach detects anomalies over multi-month dense GPS trajectories. The field instead relies on scalable sparse stay-point methods that discard this evidence, forcing separate architectures for each regime and preventing knowledge transfer. We argue this bottleneck is unnecessary: human trajectories, dense or sparse, share a natural two-dimensional cyclic structure along within-day and across-day axes. We therefore propose TITAnD (Trajectory Image Transformer for Anomaly Detection), which reformulates trajectory anomaly detection as a vision problem by representing trajectories as a Hyperspectral Trajectory Image (HTI): a day x time-of-day grid whose channels encode spatial, semantic, temporal, and kinematic information from either modality, unifying both under a single representation. Under this formulation, agent-level detection reduces to image classification and temporal localization to semantic segmentation. To model this representation, we introduce the Cyclic Factorized Transformer (CFT), which factorizes attention along the two temporal axes, encoding the cyclic inductive bias of human routines, while reducing attention cost by orders of magnitude and enabling dense multi-month anomaly detection for the first time. Empirically, TITAnD achieves the best AUC-PR across sparse and dense benchmarks, surpassing vision models like UNet while being 11-75x faster than the Transformer with comparable memory, demonstrating that vision reformulation and structure-aware modeling are jointly essential. Code will be made public soon.