Hierarchical sparse brain network estimation

Brain networks explore the dependence relationships between brain regions under consideration through the estimation of the precision matrix. An approach based on linear regression is adopted here for estimating the partial correlation matrix from functional brain imaging data. Knowing that brain networks are sparse and hierarchical, the l₁-norm penalized regression has been used to estimate sparse brain networks. Although capable of including the sparsity information, the l₁-norm penalty alone doesn´t incorporate the hierarchical structure prior information when estimating brain networks. In this paper, a new l₁ regularization method that applies the sparsity constraint at hierarchical levels is proposed and its implementation described. This hierarchical sparsity approach has the advantage of generating brain networks that are sparse at all levels of the hierarchy. The performance of the proposed approach in comparison to other existing methods is illustrated on real fMRI data.