Efficient and Scalable Granular-ball Graph Coarsening Method for Large-scale Graph Node Classification

Abstract

Graph Convolutional Network (GCN) is a model that can effectively handle graph data tasks and has been successfully applied. However, for large-scale graph datasets, GCN still faces the challenge of high computational overhead, especially when the number of convolutional layers in the graph is large. Currently, there are many advanced methods that use various sampling techniques or graph coarsening techniques to alleviate the inconvenience caused during training. However, among these methods, some ignore the multi-granularity information in the graph structure, and the time complexity of some coarsening methods is still relatively high. In response to these issues, based on our previous work, in this paper, we propose a new framework called Efficient and Scalable Granular-ball Graph Coarsening Method for Large-scale Graph Node Classification. Specifically, this method first uses a multi-granularity granular-ball graph coarsening algorithm to coarsen the original graph to obtain many subgraphs. The time complexity of this stage is linear and much lower than that of the exiting graph coarsening methods. Then, subgraphs composed of these granular-balls are randomly sampled to form minibatches for training GCN. Our algorithm can adaptively and significantly reduce the scale of the original graph, thereby enhancing the training efficiency and scalability of GCN. Ultimately, the experimental results of node classification on multiple datasets demonstrate that the method proposed in this paper exhibits superior performance. The code is available at https://anonymous.4open.science/r/1-141D/.

Figures (5)

• Figure 1: The neighborhood expansion difference between traditional GCN and our proposed method. The red node is the starting node for neighborhood nodes expansion. The traditional GCN has an exponential neighborhood expansion problem, while our method can limit the scope of neighborhood expansion by capturing multi-granularity structural information in the graph from coarse-grained to fine-grained.
• Figure 2: The framework of our proposed GB-CGNN algorithm. (1) In the Adaptive Granular-ball Coarsening Graph Formation module, we split the coarsest granular-ball from coarse-grained to fine-grained based on the adaptive splitting condition to obtain the granular-ball coarsening graph, where each granular-ball corresponds to each subgraph of the original graph. (2) In the Training GCN with Granular-ball Coarsening Graph module, we randomly sampled some granular-balls and trained them with GCN, ultimately obtaining the results of node classification.
• Figure 3: Hyperparameter sensitivity analysis on $L, H, D$.
• Figure 4: Hyperparameter sensitivity analysis on different initial centers.
• Figure 5: The node embeddings are visualized on four datasets, with different colors representing distinct node classes.

Theorems & Definitions (1)

• proof