Fused Lasso Regression for Identifying Differential Correlations in Brain Connectome Graphs

In this paper, we propose a procedure to find differential edges between two graphs from high-dimensional data. We estimate two matrices of partial correlations and their differences by solving a penalized regression problem. We assume sparsity only on differences between two graphs, not graphs themselves. Thus, we impose an ℓ ₂ penalty on partial correlations and an ℓ ₁ penalty on their differences in the penalized regression problem. We apply the proposed procedure to finding differential functional connectivity between healthy individuals and Alzheimer's disease patients.