Fused Estimation of Sparse Connectivity Patterns From Rest fMRI—Application to Comparison of Children and Adult Brains

In this paper, we consider the problem of estimating multiple sparse, co-activated brain regions from functional magnetic resonance imaging (fMRI) observations belonging to different classes. More precisely, we propose a method to analyze similarities and differences in functional connectivity between children and young adults. Often, analysis is conducted on each class separately, and differences across classes are identified with an additional postprocessing step using adequate statistical tools. Here, we propose to rely on a generalized fused Lasso penalty, which allows us to make use of the entire data set in order to estimate connectivity patterns that are either shared across classes, or specific to a given group. By using the entire population during the estimation, we hope to increase the power of our analysis. The proposed model falls in the category of population-wise matrix decomposition, and a simple and efficient alternating direction method of multipliers algorithm is introduced to solve the associated optimization problem. After validating our approach on simulated data, experiments are performed on resting-state fMRI imaging from the Philadelphia neurodevelopmental cohort data set, comprised of normally developing children from ages 8 to 21. Developmental differences were observed in various brain regions, as a total of three class-specific resting-state components were identified. Statistical analysis of the estimated subject-specific features, as well as classification results (based on age groups, up to 81% accuracy, $n = 583$ samples) related to these components demonstrate that the proposed method is able to properly extract meaningful shared and class-specific sub-networks.