Accurately modelling the resting-state functional connectivity with eigen-based connected-graph diffusion model

Understanding how functional dynamics emerge from the brain’s underlying structural architecture remains a fundamental challenge in neuroscience. Conventional graph diffusion (GD) models are limited by sparse anatomical connectivity, leading to a failure to capture indirect connectivity and negatively correlated relationships. To overcome these challenges, we introduce hypergraphs and deep neural networks to enhance the representation of brain connectivity. Specifically, graphs and hypergraphs are integrated to construct a connected-graph, providing a comprehensive representation of inter-regional brain connectivity. The Fourier-induced deep neural network is employed to infer latent inter-regional relationships from structural connectivity by leveraging spectral features, effectively capturing both low- and high-frequency components. These deduced relationships are incorporated into the connected-graph, giving rise to a connected-graph diffusion (CD) model, which is further refined via eigen-decomposition to form an eigen-based connected-graph diffusion (ECD) model. Evaluated on 1012 subjects from the Human Connectome Project (HCP) S1200 release, the ECD model achieves a mean Pearson correlation coefficients of 0.7230 in functional connectivity (FC) prediction, outperforming the GD model (0.5513) and CD model (0.6518). The stability analysis demonstrates that the prediction of the ECD model is reliable. This work demonstrates that integrating biological mechanisms with machine learning methods can accurately model complex brain networks, with implications for neural signal processing, brain-inspired computing, and neuropsychiatric diagnosis.