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Neuroimaging is the growing area of neuroscience devoted to produce data withthe goal of capturing processes and dynamics of the human brain. We considerthe problem of inferring the brain connectivity network from time dependentfunctional magnetic resonance imaging (fMRI) scans. To this aim we propose thesymmetric graphical lasso, a penalized likelihood method with a fused typepenalty function that takes into explicit account the natural symmetricalstructure of the brain. Symmetric graphical lasso allows one to learnsimultaneously both the network structure and a set of symmetries across thetwo hemispheres. We implement an alternating directions method of multipliersalgorithm to solve the corresponding convex optimization problem. Furthermore,we apply our methods to estimate the brain networks of two subjects, onehealthy and the other affected by a mental disorder, and to compare them withrespect to their symmetric structure. The method applies once the temporaldependence characterising fMRI data has been accounted for and we compare theimpact on the analysis of different detrending techniques on the estimatedbrain networks.

Fused graphical lasso for brain networks with symmetries