Réseaux et signal : des outils de traitement du signal pour l'analyse des réseaux

Abstract : This thesis describes new tools specifically designed for the analysis of networks such as social, transportation, neuronal, protein, communication networks... These networks, along with the rapid expansion of electronic, IT and mobile technologies are increasingly monitored and measured. Adapted tools of analysis are therefore very much in demand, which need to be universal, powerful, and precise enough to be able to extract useful information from very different possibly large networks. To this end, a large community of researchers from various disciplines have concentrated their efforts on the analysis of graphs, well define mathematical tools modeling the interconnected structure of networks. Among all the considered directions of research, graph signal processing brings a new and promising vision : a signal is no longer defined on a regular n-dimensional topology, but on a particular topology defined by the graph. To apply these new ideas on the practical problems of network analysis paves the way to an analysis firmly rooted in signal processing theory. It is precisely this frontier between signal processing and network science that we explore throughout this thesis, as shown by two of its major contributions. Firstly, a multiscale version of community detection in networks is proposed, based on the recent definition of graph wavelets. Then, a network-adapted bootstrap method is introduced, that enables statistical estimation based on carefully designed graph resampling schemes.
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Nicolas Tremblay. Réseaux et signal : des outils de traitement du signal pour l'analyse des réseaux. Autre [cond-mat.other]. Ecole normale supérieure de lyon - ENS LYON, 2014. Français. ⟨NNT : 2014ENSL0938⟩. ⟨tel-01078956⟩

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