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December 2015 The discriminative functional mixture model for a comparative analysis of bike sharing systems
Charles Bouveyron, Etienne Côme, Julien Jacques
Ann. Appl. Stat. 9(4): 1726-1760 (December 2015). DOI: 10.1214/15-AOAS861


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 interest in analyzing and comparing 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 visualization 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 visualization 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.


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Charles Bouveyron. Etienne Côme. Julien Jacques. "The discriminative functional mixture model for a comparative analysis of bike sharing systems." Ann. Appl. Stat. 9 (4) 1726 - 1760, December 2015.


Received: 1 July 2014; Revised: 1 April 2015; Published: December 2015
First available in Project Euclid: 28 January 2016

zbMATH: 06560808
MathSciNet: MR3456352
Digital Object Identifier: 10.1214/15-AOAS861

Keywords: bike sharing systems , Dimension reduction , functional data , Model-based clustering , open data

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.9 • No. 4 • December 2015
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