THE DISCRIMINATIVE FUNCTIONAL MIXTURE MODEL FOR A COMPARATIVE ANALYSIS OF BIKE SHARING SYSTEMS
Résumé
Bike sharing systems (BSSs) have become a means of sustainable intermodal transport and are now proposed in many cities worldwide. Most BSSs also provide open access to their data, particularly to real-time status reports on their bike stations. The analysis of the mass of data generated by such systems is of particular interest to BSS providers to update system structures and policies. This work was motivated by the will to analyze and compare several European BSSs to identify common operating patterns in BSSs and to propose practical solutions to avoid potential issues. Our approach relies on the identification of common patterns between and within systems. To this end, a model-based clustering method, called FunFEM, for time series (or more generally functional data) is developed. It is based on a functional mixture model that allows the clustering of the data in a discriminative functional subspace. This model presents the advantage in this context to be parsimonious and to allow the visual-ization of the clustered systems. Numerical experiments confirm the good behavior of FunFEM, particularly compared to state-of-the-art methods. The application of FunFEM to BSS data from JCDecaux and the Transport for London Initiative allows us to identify 10 general patterns, including pathological ones, and to propose practical improvement strategies based on the system comparison. The visual-ization of the clustered data within the discriminative subspace turns out to be particularly informative regarding the system efficiency. The proposed methodology is implemented in a package for the R software , named funFEM, which is available on the CRAN. The package also provides a subset of the data analyzed in this work. 1. Introduction. This work was motivated by the will to analyze and compare bike sharing systems (BSSs) to identify their common strengths and weaknesses. This type of study is possible because most BSS operators, in dozens of cities worldwide, provide open access to real-time status reports on their bike stations (e.g., the number of available bikes, the number of free bike stands). The implementation of bike sharing systems is one of the urban mobility services proposed in cities across the world as an additional means
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