Detecting Brain State Changes by Geometric Deep Learning of Functional Dynamics on Riemannian Manifold

Functional resonance magnetic imaging (fMRI) technology has been widely used in understanding cognition and behavior by characterizing the functional interaction between distant brain regions. Since the network topology of functional connectivity (FC) often dynamically shifts along with the change of brain states, it is challenging to identify the change point (transition between tasks) of functional connectivity without requiring prior knowledge of experiment settings. Although striking efforts have been made to detect changes on BOLD (blood-oxygen-level-dependent) signals, little attention has been paid to characterize the trajectory of whole-brain functional connectivity, which is more closely correlated to brain state change. Since FC is essentially a symmetric positive definite (SPD) correlation matrix, we present a change point detection network (CPD-Net) tailored to (1) learn the low-dimensional geometric feature representations of whole-brain functional connectivity on the Riemannian manifold of SPD matrices, and (2) automatically detect the brain state changes on the unseen functional neuroimages. It is worth noting that our CPD-Net is a manifold-based neural network to the extent that we leverage the alignment between the known functional tasks and the stratification underlying the learned low-dimensional FC feature representation on the Riemannian manifold of SPD matrices to steer the learning of geometric patterns from functional brain networks. We have evaluated the accuracy and replicability of our CPD-Net on task-based fMRI data from HCP (human connectome project) database, where our manifold-based CPD-Net achieves more accurate and consistent results than current learning-based CPD methods.