Coherent Graphical Lasso for Brain Network Discovery

In brain network discovery, researchers are interested in discovering brain regions (nodes) and functional connections (edges) between these regions from fMRI scan of human brain. Some recent works propose coherent models to address both of these sub-tasks. However, these approaches either suffer from mathematical inconsistency or fail to distinguish direct connections and indirect connections between the nodes. In this paper, we study the problem of collective discovery of coherent brain regions and direct connections between these regions. Each node of the brain network represents a brain region, i.e., a set of voxels in fMRI with coherent activities. Each edge denotes a direct dependency between two nodes. The discovered brain network represents a Gaussian graphical model that encodes conditional independence between the activities of different brain regions. We propose a novel model, called CGLasso, which combines Graphical Lasso (GLasso) and orthogonal non-negative matrix tri-factorization (ONMtF), to perform nodes discovery and edge detection simultaneously. We perform experiments on synthetic datasets with ground-truth. The results show that the proposed method performs better than the compared baselines in terms of four quantitative metrics. Besides, we also apply the proposed method and other baselines on the real ADHD-200 fMRI dataset. The results demonstrate that our method produces more meaningful networks comparing with other baseline methods.