Analyse de réseaux temporels par des méthodes de traitement du signal : application au système de vélos en libre-service à Lyon

摘要

Bike-sharing systems have become essential elements in urban transportation systems of many world's big cities. Thanks to the data generated by these systems, it is possible to obtain a precise characterization of urban cycling, both in terms of transportation and socio-economic aspects. Taking advantage of the recent abundance of data allowed by the current technology, the challenges lie in the development of efficient data analysis method, adapted to these systems. This PhD thesis proposes some answers to this issue, first by methodological developments and second by studying real-world data obtained from the bike-sharing system in Lyon, called Vélo'v.The Vélo'v system can be represented as a network, describing a set of relations between the stations spread over the city. This representation, used for many systems, enables the use of tools from network theory to measure the network structure and understand the underlying mechanisms. Nevertheless, taking into account the dynamic evolution of the structure requires an extension of the classical tools to the temporal case. Parallels between this problem and the field of signal processing can be done, and opens the way to the consideration of connections between the description of the dynamics of temporal networks and those of signals. This work introduces a duality between temporal networks and signals, such that the analysis of the signals using the classical tools of signal processing helps to the characterization of the structure of the corresponding network.This methodology, at the juncture between signal processing and network analysis, is first justified by the study of the Vélo'v network, by comparing different data analysis method and the representation of the system as a temporal network. Then, a method to relabel the vertices of the graph according to the topology of the network is discussed, opening up a duality between networks and signals. This duality is then extended to temporal networks: The analysis of the spectral properties of the signals are studied through a fully automated extraction method, enabling the decomposition of relevant network structure over time.