TGSL: Trade-off graph structure learning via multifaceted graph information bottleneck

Graph neural networks (GNNs) are prominent for their effectiveness in processing graph-structured data for semi-supervised node classification tasks. Most existing GNNs perform message passing directly based on the observed graph structure. However, in real-world scenarios, the observed structure is often suboptimal due to multiple factors, significantly degrading the performance of GNNs. To address this challenge, we first conduct an empirical analysis showing that different graph structures significantly impact empirical risk and classification performance. Motivated by our observations, we propose a novel method named Trade-off Graph Structure Learning (TGSL), guided by the multifaceted Graph Information Bottleneck (GIB) principle based on Mutual Information (MI). The key idea behind TGSL is to learn a minimal sufficient graph structure that minimizes empirical risk while maintaining performance. Specifically, we introduce global feature augmentation to capture the structural roles of nodes, and global structure augmentation to uncover global relationships between nodes. The augmented graphs are then processed by structure estimators with different parameters for refinement and redefinition, respectively. Additionally, we innovatively leverage multifaceted GIB as the optimization objective by maximizing the MI between the labels and the representation derived from the final structure, while constraining the MI between this representation and that based on the redefined structures. This trade-off helps avoid capturing irrelevant information from the redefined structures and enhances the final representation for node classification. We conduct extensive experiments across a range of datasets under clean and attacked conditions. The results demonstrate the outstanding performance and robustness of TGSL over state-of-the-art baselines.