Abstract
Common measures of brain functional connectivity (FC) including covariance and correlation matrices are symmetry-positive definite (SPD) matrices residing on a cone-shaped Riemannian manifold. Despite its remarkable success for Euclidean-valued data generation, the 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 adversarial training, conditioned on the class labels. The resulting generator can synthesize new SPD-valued FC matrices associated with different classes of brain networks, for example, 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 more realistic fMRI-based FC samples. When applied to FC data augmentation for MDD identification, classification models trained on augmented data generated by our approach achieved the largest margin of improvement in classification accuracy among the competing GANs over baselines without data augmentation.