用全局中心性替代局部度数，提升图神经网络的表示能力
Centrality Graph Shift Operators for Graph Neural Networks
- 用PageRank、k-core等全局中心性指标重构图移位算子
- 在多个真实数据集上验证算法性能优于传统方法
- 可无缝嵌入GCN、GAT等模型，适合图学习研究者
图移位算子（GSOs）如邻接矩阵和图拉普拉斯矩阵，在图论与图表示学习中具有基础作用。传统GSO通过度矩阵对邻接矩阵进行归一化，基于局部中心性。本文提出并研究了中心性图移位算子（CGSOs），使用全局中心性指标如PageRank、k-core或固定长度路径数量对邻接矩阵进行归一化。我们研究了CGSO的谱特性，以理解其对图信号的作用。通过在多个合成与真实世界数据集上定义并运行基于不同CGSO的谱聚类算法，验证了该理解。此外，我们阐述了如何将我们的CGSO作为任意图神经网络中的消息传递算子，并特别展示了使用这些CGSO的图卷积网络与图注意力网络在多个真实世界基准数据集上的优异表现。
原文摘要 · Abstract (English)
Graph Shift Operators (GSOs), such as the adjacency and graph Laplacian matrices, play a fundamental role in graph theory and graph representation learning. Traditional GSOs are typically constructed by normalizing the adjacency matrix by the degree matrix, a local centrality metric. In this work, we instead propose and study Centrality GSOs (CGSOs), which normalize adjacency matrices by global centrality metrics such as the PageRank, $k$-core or count of fixed length walks. We study spectral properties of the CGSOs, allowing us to get an understanding of their action on graph signals. We confirm this understanding by defining and running the spectral clustering algorithm based on different CGSOs on several synthetic and real-world datasets. We furthermore outline how our CGSO can act as the message passing operator in any Graph Neural Network and in particular demonstrate strong performance of a variant of the Graph Convolutional Network and Graph Attention Network using our CGSOs on several real-world benchmark datasets.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。