基于粒球计算的图粗化方法,自动寻找最优粒度以提升效率与精度。
GBGC: Efficient and Adaptive Graph Coarsening via Granular-ball Computing
- 利用粒球计算自适应划分图结构,从粗到细生成多粒度超节点。
- 处理速度提升数十至百倍,时间复杂度显著降低。
- 适用于需要高效图简化的大规模图数据预处理场景。
图粗化的目标是在保留原始图关键信息的前提下生成更小、更易处理的图。以往方法主要从谱保真角度出发,依赖预定义规则使原图与粗化后图的拉普拉斯矩阵特征值尽可能匹配。然而,这些方法忽略了图结构在不同粒度下由子区域构成的特性——高度相似且连接紧密的节点应更倾向于被聚合为粗化图中的单个节点。为此,受粒球计算在多粒度分析中应用的启发,本文提出一种新的多粒度、高效且自适应的图粗化方法(GBGC),通过自适应粒球图精炼机制,将原图从粗到细分解为不同尺寸和最优粒度的粒球,并以粒球作为超节点构建粗化图。相较于现有先进方法,该方法处理速度提升数十至百倍,时间复杂度更低。由于粒球计算具有良好的鲁棒性与泛化能力,GBGC的精度几乎始终优于原始图,具备成为标准图数据预处理方法的潜力。
原文摘要 · Abstract (English)
The objective of graph coarsening is to generate smaller, more manageable graphs while preserving key information of the original graph. Previous work were mainly based on the perspective of spectrum-preserving, using some predefined coarsening rules to make the eigenvalues of the Laplacian matrix of the original graph and the coarsened graph match as much as possible. However, they largely overlooked the fact that the original graph is composed of subregions at different levels of granularity, where highly connected and similar nodes should be more inclined to be aggregated together as nodes in the coarsened graph. By combining the multi-granularity characteristics of the graph structure, we can generate coarsened graph at the optimal granularity. To this end, inspired by the application of granular-ball computing in multi-granularity, we propose a new multi-granularity, efficient, and adaptive coarsening method via granular-ball (GBGC), which significantly improves the coarsening results and efficiency. Specifically, GBGC introduces an adaptive granular-ball graph refinement mechanism, which adaptively splits the original graph from coarse to fine into granular-balls of different sizes and optimal granularity, and constructs the coarsened graph using these granular-balls as supernodes. In addition, compared with other state-of-the-art graph coarsening methods, the processing speed of this method can be increased by tens to hundreds of times and has lower time complexity. The accuracy of GBGC is almost always higher than that of the original graph due to the good robustness and generalization of the granular-ball computing, so it has the potential to become a standard graph data preprocessing method.
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