From Euclidean to Riemannian: Boundary-Aware Geodesic Oversampling for Class-Imbalanced Graphs

Class imbalance is a widespread problem in graph-structured data. A promising solution is to oversample minority samples to balance the class distribution. However, existing methods mainly synthesize samples via Euclidean linear interpolation, which deviates from the intrinsic geometry of graph representations. Moreover, even the interpolation between intra-category samples passes through regions dominated by other categories, while improperly synthesized edges further distort the local topology. To address these limitations, we propose a $B$oundary-$A$ware $R$iemannian $G$eodesic $O$versampling method ($BARGO$) for class-imbalanced graph learning. Specifically, we first employ a Riemannian graph encoder to map nodes onto a geometry tailored to the hierarchical structures of graphs and construct Fréchet prototypes to characterize class-wise distributions. Then, we sample reliable minority seed and partner nodes, and synthesize candidate nodes along their intrinsic geodesics. Furthermore, we develop a dual screening method that evaluates both endpoint margins and intermediate points along the generation path, thereby reducing the risk of crossing category boundaries. Finally, we propose a geometry-aware topology generator. Experiments on six real-world datasets demonstrate the effectiveness of the proposed method.