Using principal curves to analyse traffic patterns on freeways

Abstract

Scatterplots of traffic speed versus flow have received considerable attention over the past decades due to their characteristic half-moon shape. Modelling data of this type is difficult as both variables are actually not a function of each other in the sense of causality, but are rather jointly generated by a third latent variable, which is a monotone function of the traffic density. We propose local principal curves (LPCs) as a tool to describe and model speed–flow data, which takes this viewpoint into account. We introduce the concept of calibration curves to determine the relationship between the latent variable (represented by the parametrisation of the principal curve) and the traffic density. We apply LPCs to a variety of speed–flow diagrams from Californian freeways, including some so far unreported patterns.