Signed Curvature Graph Representation Learning of Brain Networks for Brain Age Estimation

Graph Neural Networks (GNNs) play a pivotal role in learning representations of brain networks for estimating brain age. However, the over-squashing impedes interactions between long-range nodes, hindering the ability of message-passing mechanism-based GNNs to learn the topological structure of brain networks. Graph rewiring methods and curvature GNNs have been proposed to alleviate over-squashing. However, most graph rewiring methods overlook node features and curvature GNNs neglect the geometric properties of signed curvature. In this study, a Signed Curvature GNN (SCGNN) was proposed to rewire the graph based on node features and curvature, and learn the representation of signed curvature. First, a Mutual Information Ollivier-Ricci Flow (MORF) was proposed to add connections in the neighborhood of edge with the minimal negative curvature based on the maximum mutual information between node features, improving the efficiency of information interaction between nodes. Then, a Signed Curvature Convolution (SCC) was proposed to aggregate node features based on positive and negative curvature, facilitating the model's ability to capture the complex topological structures of brain networks. Additionally, an Ollivier-Ricci Gradient Pooling (ORG-Pooling) was proposed to select the key nodes and topology structures by curvature gradient and attention mechanism, accurately obtaining the global representation for brain age estimation. Experiments conducted on six public datasets with structural magnetic resonance imaging (sMRI), spanning ages from 18 to 91 years, validate that our method achieves promising performance compared with existing methods. Furthermore, we employed the gaps between brain age and chronological age for identifying Alzheimer's Disease (AD), yielding the best classification performance.