Revealing Functional Connectivity by Learning Graph Laplacian

Abstract

Functional connectivity (FC) has been widely used to understand how the human brain works and to discover the neurobiological underpinnings of brain disorders in many neuroscience and clinical studies. Linear FC measures such as Pearson’s correlation have been widely used in functional neuroimaging studies that are based on the observed direct or indirect electrophysiological correlates within BOLD (blood oxygen-level dependent) signals. However, there is still much to be done in the area of methods development for separation of non-linear neural and non-neural sources of signal variation. In this paper, we address this fundamental issue with a novel data-driven approach to reveal the intrinsic and reproducible FCs via graph signal processing and graph learning techniques. Specifically, we regard BOLD signals from the whole-brain as graph signals that reside on the functional network. Then, we jointly smooth the BOLD signals in the context of the brain network and optimize the network connectivity by learning the graph Laplacian that represents the network spectrum for adaptive BOLD signal smoothing. We have evaluated our novel functional network construction method on simulated brain network data and resting-state functional magnetic resonance imaging data in the study of frontotemporal dementia (FTD). Compared with the conventional correlation based methods, our proposed learning-based method shows improvements in accuracy and greater statistical power.