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

TL;DR

SATORIS-N is a novel spectral analysis framework that uses informed subspace priors and nuclear norm minimization to accurately recover traffic-density matrices from partial observations, especially under high occlusion.

Contribution

It introduces a subspace-aware SDP formulation for nuclear norm minimization that explicitly incorporates prior singular subspace information for improved traffic data imputation.

Findings

Outperforms standard matrix completion methods at high occlusion levels.

Robustly recovers traffic-density matrices with large missing data fractions.

Effective in real-world datasets from Beijing and Shanghai.

Abstract

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.