Orientation-Augmented Route Topological Representation for Trajectory Clustering

For traffic behavior analysis, trajectory clustering requires representations that make raw movement sequences comparable while suppressing irrelevant geometric variation and retaining the spatial structure needed to distinguish travel routes. Topological trajectory representations describe how paths wind around obstacles or landmarks, but flattened harmonic embeddings may not distinguish routes with similar cumulative responses and different landmark-relative orientations. We propose Azimuth-Resolved Harmonic Representation (ARHR), which supplements the cumulative harmonic embedding with a compact summary of landmark-relative angular activity. Conditional analysis gives sufficient conditions for this angular summary to distinguish trajectories with equal cumulative harmonic responses. Experiments on real-world traffic data show dataset-dependent improvements over the evaluated flattened-harmonic baseline. Weighting controls and order ablations show that clustering performance depends on the activity definition, while higher angular orders do not consistently improve clustering across datasets. These findings clarify when angular activity helps harmonic trajectory representations and support retaining this complementary structure according to the route distinctions required by the task.