SATORIS-N: Spectral Analysis based Traffic Observation Recovery via Informed Subspaces and Nuclear-norm minimization

Traffic-density matrices from different days exhibit both low rank and stable correlations in their singular-vector subspaces. Leveraging this, we introduce SATORIS-N, a framework for imputing partially observed traffic-density by informed subspace priors from neighboring days. Our contribution is a subspace-aware semidefinite programming (SDP)} formulation of nuclear norm that explicitly informs the reconstruction with prior singular-subspace information. This convex formulation jointly enforces low rank and subspace alignment, providing a single global optimum and substantially improving accuracy under medium and high occlusion. We also study a lightweight implicit subspace-alignment} strategy in which matrices from consecutive days are concatenated to encourage alignment of spatial or temporal singular directions. Although this heuristic offers modest gains when missing rates are low, the explicit SDP approach is markedly more robust when large fractions of entries are missing. Across two real-world datasets (Beijing and Shanghai), SATORIS-N consistently outperforms standard matrix-completion methods such as SoftImpute, IterativeSVD, statistical, and even deep learning baselines at high occlusion levels. The framework generalizes to other spatiotemporal settings in which singular subspaces evolve slowly over time. In the context of intelligent vehicles and vehicle-to-everything (V2X) systems, accurate traffic-density reconstruction enables critical applications including cooperative perception, predictive routing, and vehicle-to-infrastructure (V2I) communication optimization. When infrastructure sensors or vehicle-reported observations are incomplete - due to communication dropouts, sensor occlusions, or sparse connected vehicle penetration-reliable imputation becomes essential for safe and efficient autonomous navigation.

💡 Research Summary

The paper introduces SATORIS‑N, a novel framework for imputing missing entries in daily traffic‑density matrices by explicitly leveraging the stability of singular‑vector subspaces across adjacent days. The authors first observe that traffic‑density matrices, constructed by vectorizing spatial grids over hourly time slots, are both low‑rank (a rank‑k approximation captures >75 % of variance for k ≤ 10) and exhibit highly stable left and right singular subspaces from day to day. These two properties imply that subspace information from a near‑complete neighboring day can serve as a powerful prior, reducing the sample complexity required for accurate recovery.

Two complementary strategies are proposed. The “implicit subspace alignment” approach simply concatenates the target day’s matrix with a neighboring day’s matrix either horizontally (sharing spatial subspace) or vertically (sharing temporal subspace) and then applies any standard low‑rank matrix completion algorithm such as SoftImpute or IterativeSVD. This heuristic is easy to implement but can only align one subspace at a time and its benefits diminish as the missing rate grows.

The core contribution is an “explicit subspace‑aware nuclear‑norm minimization” formulated as a semidefinite program (SDP). The nuclear norm ‖X‖_* is expressed via the convex SDP
min ½(tr A + tr B)
subject to