The Macroscopic Fundamental Diagram (MFD), which exhibits the relationship between average flow and average density of an urban network, is a promising framework for monitoring and controlling urban traffic networks. Given that monitoring resources (e.g. loop detectors, probe vehicle data, etc.) are limited in real-world networks, acquiring adequate data to estimate an MFD is of crucial importance. This study presents a novel, network-wide approach to identifying critical links and estimating average traffic flow and density. The proposed model estimates the MFD using flow and density measurements from those critical links, which constitute only a small subset of all the links in the network. To find the critical links, we rely on historical probe vehicle data, and propose a model that builds on Principal Component Analysis (PCA), a dimensionality reduction and a feature selection method. Essentially, using PCA, a large number of possibly interrelated variables in a dataset can be reduced to a set of smaller uncorrelated variables, while maintaining as much information as possible in the dataset. The resulting uncorrelated variables, or the principal components, indicate the major patterns or the dominating features of the original dataset. Additionally, PCA enables the (approximate) reconstruction of the full-scale dataset from the selected features (or principal components). In this work, we apply PCA in order to identify the main traffic features from a probe vehicle dataset; then, we find the links that are associated with these features (i.e., critical links); then, we locate loop detectors on those links to collect flow and density data; and finally, we reconstruct the full-scale data, building on the PCA mechanism. This gives us the flow and density of all links, from which we can effectively estimate the MFD.

宏观基本图（MFD）展现了城市网络的平均流量和平均密度之间的关系，是用于监视和控制城市交通网络的有希望的框架。鉴于在现实世界的网络中监视资源（例如环路探测器，探测车辆数据等）受到限制，因此获取足够的数据以估算MFD至关重要。这项研究提出了一种新颖的全网络方法，用于识别关键链路并估计平均流量和密度。提出的模型使用来自那些关键链路的流量和密度测量值来估计MFD，这些关键链路仅构成网络中所有链路的一小部分。为了找到关键的链接，我们依靠历史探测车辆数据，并提出了一个基于主成分分析（PCA）的模型，降维和特征选择方法。本质上，使用PCA可以将数据集中的大量可能相互关联的变量简化为一组较小的不相关变量，同时在数据集中保留尽可能多的信息。产生的不相关变量或主要成分表示原始数据集的主要模式或主导特征。此外，PCA可以从所选要素（或主要成分）中（近似）重建完整比例数据集。在这项工作中，我们应用PCA来从探测车辆数据集中识别主要交通特征。然后，我们找到与这些功能关联的链接（即关键链接）；然后，我们在这些链路上放置环路检测器，以收集流量和密度数据；最后，我们基于PCA机制来重建全面数据。这为我们提供了所有链接的流量和密度，从中我们可以有效地估计MFD。