arXiv:2504.16360cs.LG2025-04

提出GOMKCN模型,让图神经网络更精准地分离和识别图结构特征。

Disentangled Graph Representation Based on Substructure-Aware Graph Optimal Matching Kernel Convolutional Networks

  • 将图看作节点为中心的子图,用最优匹配核进行卷积操作
  • 在多个图任务上实现更高精度与可解释性,显著优于现有方法
  • 适合需要理解图结构内在模式的研究者或工程师

图能有效表征关系数据,推动图表示学习方法发展以挖掘潜在预测信息。当前主流图神经网络(GNNs)支持端到端学习,而最新解耦图表示学习通过分离图数据中的独立因素提升可解释性。然而,现有方法常隐式且粗粒度刻画图结构,限制了对图内结构模式的分析。本文提出图最优匹配核卷积网络(GOMKCN),将图视为以节点为中心的子图,每个子图作为编码位置特异性信息的结构因子,将图预测转化为结构模式识别。受卷积神经网络启发,GOMKCN引入图最优匹配核(GOMK)作为卷积算子,计算子图与可学习图滤波器之间的相似性。数学上,GOMK将子图与滤波器映射到希尔伯特空间,将图表示为点集。解耦表示通过将子图投影到任务优化的滤波器上生成,滤波器通过梯度下降自适应捕捉相关结构模式。关键在于,GOMK在相似性度量中融入局部对应关系,解决了图核中可微性与准确性的权衡问题。实验验证,GOMKCN在图模式挖掘与预测任务中均取得更优精度与可解释性,推动了解耦图表示学习的理论基础。

原文摘要 · Abstract (English)

Graphs effectively characterize relational data, driving graph representation learning methods that uncover underlying predictive information. As state-of-the-art approaches, Graph Neural Networks (GNNs) enable end-to-end learning for diverse tasks. Recent disentangled graph representation learning enhances interpretability by decoupling independent factors in graph data. However, existing methods often implicitly and coarsely characterize graph structures, limiting structural pattern analysis within the graph. This paper proposes the Graph Optimal Matching Kernel Convolutional Network (GOMKCN) to address this limitation. We view graphs as node-centric subgraphs, where each subgraph acts as a structural factor encoding position-specific information. This transforms graph prediction into structural pattern recognition. Inspired by CNNs, GOMKCN introduces the Graph Optimal Matching Kernel (GOMK) as a convolutional operator, computing similarities between subgraphs and learnable graph filters. Mathematically, GOMK maps subgraphs and filters into a Hilbert space, representing graphs as point sets. Disentangled representations emerge from projecting subgraphs onto task-optimized filters, which adaptively capture relevant structural patterns via gradient descent. Crucially, GOMK incorporates local correspondences in similarity measurement, resolving the trade-off between differentiability and accuracy in graph kernels. Experiments validate that GOMKCN achieves superior accuracy and interpretability in graph pattern mining and prediction. The framework advances the theoretical foundation for disentangled graph representation learning.

图神经网络解耦表示结构识别

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