Highway traffic state data collected from a network of sensors can be considered as a high-dimensional nonlinear dynamical system. In this paper, we develop a novel data-driven method–anti-circulant dynamic mode decomposition with sparsity-promoting (circDMDsp)–to study the dynamics of highway traffic speed data. Particularly, circDMDsp addresses several issues that hinder the application of existing DMD models: limited spatial dimension, presence of both recurrent and non-recurrent patterns, high level of noise, and known mode stability. The proposed circDMDsp framework allows us to numerically extract spatial–temporal coherent structures with physical meanings/interpretations: the dynamic modes reflect coherent spatial bases, and the corresponding temporal patterns capture the temporal oscillation/evolution of these dynamic modes. Our result based on Seattle highway loop detector data showcases that traffic speed data is governed by a set of periodic components, e.g., mean pattern, daily pattern, and weekly pattern, and each of them has a unique spatial structure. The spatiotemporal patterns can also be used to recover/denoise observed data and predict future values at any timestamp by extrapolating the temporal Vandermonde matrix. Our experiments also demonstrate that the proposed circDMDsp framework is more accurate and robust in data reconstruction and prediction than other DMD-based models. The code for the algorithm and experiment is available at https://github.com/mcgill-smart-transport/circDMDsp.

从传感器网络收集的公路交通状态数据可被视为高维非线性动力系统。在本文中，我们开发了一种新的数据驱动方法——具有稀疏性促进的反循环动态模式分解 (circDMDsp)——来研究高速公路交通速度数据的动态。特别是，circDMDsp 解决了阻碍现有 DMD 模型应用的几个问题：有限的空间维度、循环和非循环模式的存在、高噪声水平和已知模式稳定性。所提出的 circDMDsp 框架允许我们从数值上提取具有物理意义/解释的时空相干结构：动态模式反映相干空间基础，相应的时间模式捕获这些动态模式的时间振荡/演化。我们基于西雅图高速公路环路检测器数据的结果表明，交通速度数据由一组周期性成分控制，例如平均模式、每日模式和每周模式，并且它们中的每一个都具有独特的空间结构。时空模式还可以用于恢复/去噪观察到的数据，并通过外推时间范德蒙矩阵来预测任何时间戳的未来值。我们的实验还表明，所提出的 circDMDsp 框架在数据重建和预测方面比其他基于 DMD 的模型更准确和稳健。算法和实验的代码可在 时空模式还可以用于恢复/去噪观察到的数据，并通过外推时间范德蒙矩阵来预测任何时间戳的未来值。我们的实验还表明，所提出的 circDMDsp 框架在数据重建和预测方面比其他基于 DMD 的模型更准确和稳健。算法和实验的代码可在 时空模式还可以用于恢复/去噪观察到的数据，并通过外推时间范德蒙矩阵来预测任何时间戳的未来值。我们的实验还表明，所提出的 circDMDsp 框架在数据重建和预测方面比其他基于 DMD 的模型更准确和稳健。算法和实验的代码可在https://github.com/mcgill-smart-transport/circDMDsp。