Traffic speed is central to characterizing the fluidity of the road network. Many transportation applications rely on it, such as real-time navigation, dynamic route planning, and congestion management. Rapid advances in sensing and communication techniques make traffic speed detection easier than ever. However, due to sparse deployment of static sensors or low penetration of mobile sensors, speeds detected are incomplete and far from network-wide use. In addition, sensors are prone to error or missing data due to various kinds of reasons, speeds from these sensors can become highly noisy. These drawbacks call for effective techniques to recover credible estimates from the incomplete data. In this work, we first identify the issue as a spatiotemporal kriging problem and propose a Laplacian enhanced low-rank tensor completion (LETC) framework featuring both lowrankness and multi-dimensional correlations for large-scale traffic speed kriging under limited observations. To be specific, three types of speed correlation including temporal continuity, temporal periodicity, and spatial proximity are carefully chosen and simultaneously modeled by three different forms of graph Laplacian, named temporal graph Fourier transform, generalized temporal consistency regularization, and diffusion graph regularization. We then design an efficient solution algorithm via several effective numeric techniques to scale up the proposed model to network-wide kriging. By performing experiments on two public million-level traffic speed datasets, we finally draw the conclusion and find our proposed LETC achieves the state-of-the-art kriging performance even under low observation rates, while at the same time saving more than half computing time compared with baseline methods. Some insights into spatiotemporal traffic data modeling and kriging at the network level are provided as well.

翻译：交通速度是表征路网流动性的核心指标，许多交通应用（如实时导航、动态路径规划和拥堵管理）均依赖于此。传感与通信技术的飞速发展使得交通速度检测比以往更加便捷。然而，由于静态传感器部署稀疏或移动传感器渗透率低，检测到的速度数据不完整且远未达到全网覆盖水平。此外，传感器因各类原因易出错或缺失数据，导致速度数据高度噪声化。这些缺陷要求我们开发有效的技术手段从不完整数据中恢复可靠估计。本文首先将问题界定为时空克里金问题，并提出一种拉普拉斯增强的低秩张量补全（LETC）框架，该框架兼具低秩性和多维相关性，适用于有限观测下的大规模交通速度克里金。具体而言，我们精心选取了三种速度相关性（包括时间连续性、时间周期性和空间邻近性），并通过三种不同形式的图拉普拉斯（即时间图傅里叶变换、广义时间一致性正则化和扩散图正则化）对其进行同步建模。随后，我们利用多种高效数值技术设计了求解算法，将所提模型扩展至全网克里金。通过在两个百万级公开交通速度数据集上进行实验，最终得出结论：即使在低观测率条件下，我们提出的LETC方法仍能达到最先进的克里金性能，同时相比基线方法节省超过一半的计算时间。此外，本文还提供了关于网络级时空交通数据建模与克里金的一些见解。