Multi-Scale Factor Analysis of High-Dimensional Functional Connectivity in Brain Networks

We consider challenges in modeling and estimating high-dimensional functional connectivity in brain networks with a large number of nodes arranged in a hierarchical and modular structure. We develop a multi-scale factor analysis (MSFA) model which partitions the massive neuroimaging time series data defined over the brain networks into a finite set of regional clusters. To achieve further dimension reduction, signals in each cluster are represented by a small number of latent factors. The correlation matrix for all nodes in the network can be approximated by lower-dimensional sub-structures derived from the cluster-specific factors. This enables a reliable and computationally efficient multi-scale analysis of both regional and global network connectivity. To estimate regional connectivity between numerous nodes (within each cluster), we apply principal components analysis (PCA) to extract the factors. Then, we estimate global connectivity (between clusters or sub-networks) based on the factors across regions using the RV-coefficient as the cross-dependence measure. Simulation results show that the proposed MSFA estimator improves accuracy of connectivity estimation in high-dimensional settings. When applied to resting-state functional magnetic resonance imaging (fMRI) data, our method identifies modular structure of resting-state networks at multiple scales, revealing interesting connectivity patterns between voxels, regions of interest (ROIs), and functional networks.