arXiv:2602.03138cs.LG2026-02

利用邻日子空间先验,提升交通密度缺失数据的恢复精度。

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

  • 基于邻日奇异子空间先验,设计凸优化框架实现低秩与子空间对齐联合约束。
  • 在中高缺失率下,相比传统方法误差降低20%以上,全局最优解保证精度。
  • 适用于智能网联汽车等基础设施感知不全场景,助力自动驾驶安全导航。

不同日期的交通密度矩阵具有低秩性及奇异向量子空间的稳定性。基于此,我们提出SATORIS-N框架,通过邻日信息引导的子空间先验来填补部分缺失的交通密度数据。其核心是将核范数重构问题建模为一种显式融入奇异子空间先验的半定规划(SDP)形式,该凸模型同时强制低秩性与子空间对齐,获得唯一全局最优解,在中高缺失率下显著提升精度。此外,还探索了一种轻量级隐式子空间对齐策略:将连续日数据拼接以促进时空奇异方向对齐。当缺失率较低时,该启发式方法收益有限;而显式SDP方法在大量数据缺失时表现更稳健。在北京市和上海市两个真实数据集上,SATORIS-N持续优于SoftImpute、IterativeSVD、统计方法及深度学习基线,在高缺失场景下性能领先。该框架可推广至奇异子空间缓慢演化的其他时空场景。在智能车辆与车联万物(V2X)系统中,精确的交通密度重建支持协同感知、预测路径规划及车路通信优化。当基础设施传感器或车载上报数据因通信中断、传感器遮挡或联网车辆稀疏而缺失时,可靠的补全对保障自主导航的安全与高效至关重要。

原文摘要 · Abstract (English)

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.

交通重建矩阵补全子空间对齐智能交通

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