Graph-Regularized Manifold-Aware Conditional Wasserstein GAN for Brain Functional Connectivity Generation

作者：Yee Fan Tan, Chee‐Ming Ting, Fuad Noman, Raphaël C. -W. Phan, Hernando Ombao · 发表于：arXiv (Cornell University) · 年份：2022 · DOI：10.48550/arxiv.2212.05316 · 被引用次数：8 · 研究领域：Functional Brain Connectivity Studies、Mental Health Research Topics、Neural dynamics and brain function

Common measures of brain functional connectivity (FC) including covariance and correlation matrices are semi-positive definite (SPD) matrices residing on a cone-shape Riemannian manifold. Despite its remarkable success for Euclidean-valued data generation, use of standard generative adversarial networks (GANs) to generate manifold-valued FC data neglects its inherent SPD structure and hence the inter-relatedness of edges in real FC. We propose a novel graph-regularized manifold-aware conditional Wasserstein GAN (GR-SPD-GAN) for FC data generation on the SPD manifold that can preserve the global FC structure. Specifically, we optimize a generalized Wasserstein distance between the real and generated SPD data under an adversarial training, conditioned on the class labels. The resulting generator can synthesize new SPD-valued FC matrices associated with different classes of brain networks, e.g., brain disorder or healthy control. Furthermore, we introduce additional population graph-based regularization terms on both the SPD manifold and its tangent space to encourage the generator to respect the inter-subject similarity of FC patterns in the real data. This also helps in avoiding mode collapse and produces more stable GAN training. Evaluated on resting-state functional magnetic resonance imaging (fMRI) data of major depressive disorder (MDD), qualitative and quantitative results show that the proposed GR-SPD-GAN clearly outperforms several state-of-the-art GANs in generating mo...