Recherche de la connectivité de réseaux complexes. Application en fMRI

We consider random processes indexed by complex networks. A signal is recorded at each node of the network, and the problem adressed here is the recovery of the connectivity of the network from the signals measured. A first analysis consists in studying pairwise correlations to determine the nodes that share information. In a second step, correlated nodes are examined using partial correlation in order to eliminate cofounders. Moreover, all the analysis is performed on the wavelet coefficients for each band. The wavelet decomposition is adopted to eliminate the long memory property that characterizes the signals we study. To end, we apply the methodology to the analysis of data issued from functional magnetic resonance imaging of the brain.