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

TL;DR

This work tackles the challenge of imputing missing traffic-density data in V2X-enabled environments by exploiting the low-rank structure and cross-day stability of traffic matrices. It introduces SATORIS-N, a subspace-aware framework that combines implicit priors from neighboring days with an explicit semidefinite program (SDP) formulation of the nuclear norm to inject known singular-subspace information. The explicit SDP variants (HRESI, SRESI, SRRSI, SRWSI) achieve robust improvements under high occlusion, while a lightweight implicit approach provides gains at lower missingness; across Beijing and Shanghai datasets, SATORIS-N consistently outperforms classical and deep-learning baselines, with substantial reductions in RRMSE/MAE at missing rates up to 90%. The authors also quantify cross-day subspace stability, provide reproducible open-source code, and discuss practical implications for V2X cooperative perception and autonomous navigation in sparse-sensing scenarios.

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.

Figures (6)

• Figure 1: Image imputation using vanilla nuclear norm minimization and subspace informed nuclear norm minimization. nnorm is vanilla nuclear norm minimization and nnmorm-ssi is subspace informed nuclear norm minimization using hard reconstruction (HRESI). Images are from sklearn load_sample_images().
• Figure 2: Spatial and temporal averages over a single 24-hour day in the Beijing and Shanghai datasets.
• Figure 3: Stability of left and right singular subspaces for Beijing and Shanghai across adjacent days using the subspace-overlap metric in (\ref{['eq:subspace_overlap_metric']}); $0$ = orthogonal, $1$ = perfectly aligned.
• Figure 4: Comparison of Relative Root Means Square Error (RRMSE) for 10 imputation algorithms and their implicit subspace-informed variants across varying missing percentages (mp) for Shanghai dataset. The top row is the baseline, the second the -h (proposed horizontal stacking) and the last -v (proposed vertical stacking) variant. Implicit priors yields performance gains, especially under moderate to high occlusion. Gains are more pronounced for vertical stacking (-h) since that allows shared spatial subspaces v.s temporal in horizontal stacking (-v). Highlighted NNmin-h/SRSI is comparable and relates to our other explicitly informed subspace-aware nuclear norm based imputation methods
• Figure 5: RRMSE comparison within proposed nuclear norm based algorithms: Explicit subspace-informed methods SRESI, SRESI, SRRSI, and SRWSI with other nuclear norm methods like NNmin, SoftImpute/Softimpute-h on Shanghai (top) and Beijing (bottom). All our methods, except SRWSI, improve imputation performance at high occlusion levels (above 75%).