Graph Coarsening via Supervised Granular-Ball for Scalable Graph Neural Network Training

TL;DR

This paper constructs a coarsened graph network by iteratively splitting the graph into granular-balls based on a purity threshold and using these granular-balls as super vertices using granular-balls as super vertices to effectively compress graph data.

Abstract

Graph Neural Networks (GNNs) have demonstrated significant achievements in processing graph data, yet scalability remains a substantial challenge. To address this, numerous graph coarsening methods have been developed. However, most existing coarsening methods are training-dependent, leading to lower efficiency, and they all require a predefined coarsening rate, lacking an adaptive approach. In this paper, we employ granular-ball computing to effectively compress graph data. We construct a coarsened graph network by iteratively splitting the graph into granular-balls based on a purity threshold and using these granular-balls as super vertices. This granulation process significantly reduces the size of the original graph, thereby greatly enhancing the training efficiency and scalability of GNNs. Additionally, our algorithm can adaptively perform splitting without requiring a predefined coarsening rate. Experimental results demonstrate that our method achieves accuracy comparable to training on the original graph. Noise injection experiments further indicate that our method exhibits robust performance. Moreover, our approach can reduce the graph size by up to 20 times without compromising test accuracy, substantially enhancing the scalability of GNNs.

Figures (7)

• Figure 1: Comparing original graph training with coarsening training. The coarsening approach reduces graph complexity while preserving key structural and label information, improving graph neural network training efficiency.
• Figure 2: The overview of the SGBGC architecture. Our method consists of four stages: coarse partitioning, fine-grained splitting, granular-ball graph construction, and GNN training on the coarsened graph. In the coarse partitioning stage, the graph is divided into $\sqrt{N}$ clusters, where $N$ is the total number of nodes, with each cluster evenly divided based on label categories. The fine-grained splitting stage divides clusters further based on granular-ball quality until the specified threshold is reached. Finally, the granular-ball graph is constructed and used for GNN training to produce coarsened embeddings.
• Figure 3: Comparison of time costs among different coarsening methods.
• Figure 4: Comparison of different noise rates on Citeseer with 0.3 coarsening ratio, including original graph and various coarsening methods.
• Figure 5: The memory usage of APPNP and granular-ball coarsened APPNP.

Theorems & Definitions (4)

• Definition 3: Label Consistency Measure
• Definition 4: Rayleigh Quotient for Granular-Ball Graph
• Theorem 1
• proof