Title: Adaptive Granularity Graph Rewiring via Granular-ball for Graph Clustering
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Clustering, Graph Rewiring, Graph Neural Network, Multi-Granularity Cognitive Computing

Abstract: Graph clustering aims to partition a graph into homogeneous groups of nodes, capturing the graph's node features and connectivity structure. Graph neural network-based approaches excel in node clustering by leveraging the homophilic assumption, which posits that neighboring nodes are likely to share similar characteristics, but low-homophily edges can introduce noise, potentially reducing clustering accuracy. Previous work rewires connections by estimating homophily at an overly fine granular, primarily based on the similarity of connected nodes. Nevertheless, they largely neglect the fact that homophily is distributed across multiple granular levels within the graph. Considering the multi-granular nature of the homophily distribution, we could better differentiate between homophilic and heterophilic nodes at the optimal granularity. To this end, we propose a novel Adaptive Granular Graph Rewiring method (AGGR) that adaptively identifies homophilic regions at appropriate granularities and subtly enhances homophily within the graph structure through graph rewiring, significantly improving GNN performance and clustering outcomes. Specifically, AGGR introduces an Adaptive Granular-Ball graph refinement mechanism to capture homophilic structures within graphs. In addition, a Multi-Granularity Graph Rewiring method is further proposed to add highly homophilic social relations intra-homophilic domains and cut low homophilic relations inter-them. Moreover, we propose a Multi-Task Homophily Refinement Learning framework to integrate the optimization of graph rewiring with graph clustering. Extensive experiments conducted on benchmark datasets demonstrate that AGGR outperforms the state-of-the-art method.