Learning Graph Filters for Structure-Function Coupling based Hub Node Identification

Over the past two decades, tools from network science have been leveraged to characterize the organization of both structural and functional brain networks. One such tool is hub node identification. Hubs are nodes within a network that link distinct brain units corresponding to specialized functional processes. Conventional methods for identifying hubs utilize different types of centrality measures and participation coefficient to profile various aspects of nodal importance. These methods solely rely on the functional connectivity networks constructed from functional magnetic resonance imaging (fMRI), ignoring the structure-function coupling in the brain. In this paper, we introduce a graph signal processing (GSP) based framework that utilizes both the structural connectivity and the functional activation to identify hubs. The proposed framework models functional activity as graph signals on the structural connectivity. Hub nodes are then detected based on the premise that they are sparse, have higher level of activity compared to their neighbors, and the non-hub nodes' activity is the output of a low-pass graph filter. Based on these assumptions, an optimization framework, GraFHub, is formulated to learn the coefficients of the optimal graph filter and detect the hub nodes. The proposed framework is evaluated on both simulated data and resting state fMRI (rs-fMRI) data from Human Connectome Project (HCP).