The formation will cover advanced data analysis, from methods in statistical signal processing up to the recent evolutions in machine learning. 

These lectures will cover modern techniques in signal processing for data which are distributed over networks. 

Analysis of data over networks or graphs (also called graph signals) is currently a very active research domain, and we will study approaches combining signal and image processing, graph theory (especially algebraic methods such as spectral analysis of graphs), and distributed methods on networks. The application of signal processing for networks ranges from the study of technological networks (of sensors, in telecommunication or transport) to more general complex networks such as biological or social networks. 

Three main topics will be explored. First, harmonic analysis on graphs will be discussed, going from simple Fourier transform suited to graph signals to multi-scale wavelet analysis. Second variational approaches on graphs will be discussed, allowing to design methods such as denoising, restoration, inference or clustering on graphs. For this purpose, modern optimization approaches based on monotone operators will also be introduced. Finally, distributed methods will be considered, especially for consensus, estimation or detection in a network, including methods using distributed optimization.

Ces dernières années, la modélisation des systèmes sociaux a connu une forte expansion. Le nombre de publications a été multiplié par dix en cinq ans. Les raisons sont multiples, allant de l'importance des applications possibles, la disponibilité de plus en plus grande de données numérisées (localisations, Internet, publications, téléphones portables, vélov ...) ainsi que la puissance des ordinateurs et outils mathématiques pour analyser les grandes bases de données.

Le stage de recherche dure au minimum 24 semaines de début février à fin juillet.
Un projet de stage devra être déposé par chaque étudiant.e avant le 15 décembre.

Soutenances des stages : début septembre