We develop a topological analysis of robust traffic pace patterns using persistent homology. We develop Rips filtrations, parametrized by pace, for a symmetrization of traffic pace along the (naturally) directed edges in a road network. Our symmetrization is inspired by recent work of Turner (2019 Algebr. Geom. Topol. 19 1135–1170). Our goal is to construct barcodes which help identify meaningful pace structures, namely connected components or ‘rings’. We develop a case study of our methods using datasets of Manhattan and Chengdu traffic speeds. In order to cope with the computational complexity of these large datasets, we develop an auxiliary application of the directed Louvain neighborhood-finding algorithm. We implement this as a preprocessing step prior to our main persistent homology analysis in order to coarse-grain small topological structures. We finally compute persistence barcodes on these neighborhoods. The persistence barcodes have a metric structure which allows us to both qualitatively and quantitatively compare traffic networks. As an example of the results, we find robust connected pace structures near Midtown bridges connecting Manhattan to the mainland.

我们使用持续的同源性开发了鲁棒的交通速度模式的拓扑分析。我们开发了按速度参数化的Rips过滤，以使沿道路网络中（自然）定向边缘的交通速度对称化。我们的对称是最近特纳的作品（2019启发Algebr。的Geom。白杨。 191135–1170）。我们的目标是构建有助于识别有意义的步速结构的条形码，即连接的组件或“环”。我们使用曼哈顿和成都的行车速度数据集来开发我们的方法的案例研究。为了应付这些大型数据集的计算复杂性，我们开发了有向Louvain邻域查找算法的辅助应用程序。在对主要持久性同源性进行分析之前，我们将其作为预处理步骤实施，以粗化小拓扑结构。最后，我们在这些邻域上计算持久性条形码。持久性条形码具有一种度量结构，使我们能够定性和定量地比较交通网络。作为结果的一个例子，