Topological Analysis of Traffic Pace via Persistent Homology

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. 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.