Graph Condensation via Homophily Node Refining and Fine-Grained Distribution Matching

The remarkable success of GNNs has provoked the challenge of high computational and memory overhead when training with large-scale graphs. As a promising solution, graph condensation is committed to constructing synthetic graphs with significantly smaller size, which are expected to preserve the essential characteristics of the original ones. During this process, a core problem is how to accurately portray and align the data distribution structures between the original graph space and the synthetic graph space. A mainstream idea in existing research is matching the class distributions between the two spaces. Unfortunately, they generally overlook two key issues: 1) heterophilic nodes in original graphs may render the chaotic class distribution patterns; 2) coarse-grained matching of the overall class centroid between original and synthetic spaces is insufficient for data with complex subcategory distributions. In this paper, we propose a novel Graph Condensation method via homophily node Refinement and fine-grained class Distribution matching (GCRD). Given the original large-scale graph, we first distinguish the nodes into advantageous homophilic nodes and detrimental heterophilic nodes, followed by adaptively assigning node weights to refine the generated class distribution patterns of the original graphs. Furthermore, with the refined class distribution patterns, we propose a fine-grained distribution matching objective to more delicately align the local distribution structure of subclasses within each class. The rigorous theoretical analysis confirms the effectiveness of our proposal in precisely learning the class information. Extensive experiments demonstrate our state-of-the-art classification and cross-architecture generalization performance against various baselines.