Uncovering shape signatures of resting-state functional connectivity by geometric deep learning on Riemannian manifold.
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Abstract
Functional neural activities manifest geometric patterns, as evidenced by the evolving network topology of functional connectivities (FC) even in the resting state. In this work, we propose a novel manifold-based geometric neural network for functional brain networks (called “Geo-Net4Net” for short) to learn the intrinsic low-dimensional feature representations of resting-state brain networks on the Riemannian manifold. This tool allows us to answer the scientific question of how the spontaneous fluctuation of FC supports behavior and cognition. We deploy a set of positive maps and rectified linear unit (ReLU) layers to uncover the intrinsic low-dimensional feature representations of functional brain networks on the Riemannian manifold taking advantage of the symmetric positive-definite (SPD) form of the correlation matrices. Due to the lack of well-defined ground truth in the resting state, existing learning-based methods are limited to unsupervised methodologies. To go beyond this boundary, we propose to self-supervise the feature representation learning of resting-state functional networks by leveraging the task-based counterparts occurring before and after the underlying resting state. With this extra heuristic, our Geo-Net4Net allows us to establish a more reasonable understanding of resting-state FCs by capturing the geometric patterns (aka. spectral/shape signature) associated with resting states on the Riemannian manifold. We have conducted extensive experiments on both simulated data and task-based functional resonance magnetic imaging (fMRI) data from the Human Connectome Project (HCP) database, where our Geo-Net4Net not only achieves more accurate change detection results than other state-of-the-art counterpart methods but also yields ubiquitous geometric patterns that manifest putative insights into brain function.© 2022 The Authors. Human Brain Mapping published by Wiley Periodicals LLC.