Detecting Transportation Mode Using Dense Smartphone GPS Trajectories and Transformer Models

Trajectory anomaly detection underpins applications from fraud detection to urban mobility analysis. Dense GPS preserves fine-grained evidence such as abnormal speeds and short-duration events, but its quadratic cost makes multi-month analysis intractable; sparse stay-point methods scale by discarding that evidence and require a separate modeling regime. We argue that this bottleneck is unnecessary: dense and sparse trajectories share a natural two-dimensional cyclic structure along within-day and across-day axes. TITAnD (Trajectory Image Transformer for Anomaly Detection) is the first framework to cast both in a single representation, a Hyperspectral Trajectory Image (HTI), a day $\times$ time-of-day grid whose channels encode spatial, semantic, temporal, and kinematic information. Under this formulation, agent-level detection reduces to image classification and temporal localization to semantic segmentation. The Cyclic Factorized Transformer (CFT) models the two temporal axes directly, reducing attention cost by up to two orders of magnitude. With the HTI, multi-month dense anomaly detection becomes feasible for the first time, and CFT keeps it accurate and fast. Empirically, TITAnD matches or beats every evaluated baseline in AUC-PR on all four benchmarks. It surpasses vision models such as U-Net while using as few as 6.5M parameters, and it runs 11--75$\times$ faster than a capacity-matched flat Transformer on the same trajectory images.

Learning generalizable trajectory representations from raw GPS traces remains difficult because the data is continuous, noisy, and irregularly sampled. Spatial tokenization is also challenging: fine grids yield sparse cells with weak embeddings, while coarse grids merge heterogeneous movement patterns into the same token. We present TrajTok, a trajectory encoder with a simple pretraining recipe for transferable trajectory embeddings. TrajTok first learns a multi-resolution hexagonal cell partition from the spatial distribution of GPS points, converting noisy GPS sequences into discrete cell tokens. To capture both geometry and kinematics, it uses a factorized transformer encoder with early per-modality self-attention blocks, cross-attention fusion layers, and spatiotemporal rotary position embeddings, ST-RoPE, to encode where and when each token occurs. TrajTok is pretrained with masked-token modeling that recovers both geometric structure and kinematic patterns from partial trajectory observations. On the Porto dataset, a frozen TrajTok encoder with lightweight task adapters achieves strong performance across trajectory similarity search, classification, estimated time of arrival, and full travel-time regression, outperforming multiple task-specific methods. The same frozen encoder supports both geometry-dominated and kinematics-dominated tasks, suggesting that TrajTok learns transferable trajectory structure rather than task-specific shortcuts. These results indicate that learned multi-resolution spatial tokenization combined with masked-token pretraining is a promising direction for general-purpose trajectory foundation models.

We present a training-free method for multi-modal trajectory prediction that achieves comparable accuracy to a 57M-parameter transformer while requiring no GPU and zero learned parameters. The method builds a transition table of historical state-to-next position pairs and retrieves neighbors using a product kernel over spatial proximity, bearing, speed, and temporal context. Two inference modes operate over this shared representation: diversity-penalized sampling produces trajectories covering distinct plausible routes, while beam search finds the highest-likelihood path. On the TrAISformer benchmark (Danish Maritime AIS), our method achieves competitive accuracy at full data availability and dramatically outperforms the transformer in data-scarce regimes---remaining stable down to 10% of training data where TrAISformer degrades catastrophically. This enables deployment in new geographic regions from an order of magnitude less historical data.