论文标题
密集和稀疏图上图神经网络的光谱分析
A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphs
论文作者
论文摘要
在这项工作中，我们提出了一个随机图模型，该模型可以在不同级别的稀疏度中产生图形。我们分析了稀疏性如何影响图光谱，从而在致密和稀疏图上的节点分类中表现出图神经网络（GNN）的性能。我们将GNN与已知的光谱方法进行比较，这些光谱方法可提供一致的估计量，以在密集图上进行社区检测，这是一项密切相关的任务。我们表明，GNN可以在稀疏图上胜过光谱方法，并在合成图和真实图上使用数值示例来说明这些结果。
In this work we propose a random graph model that can produce graphs at different levels of sparsity. We analyze how sparsity affects the graph spectra, and thus the performance of graph neural networks (GNNs) in node classification on dense and sparse graphs. We compare GNNs with spectral methods known to provide consistent estimators for community detection on dense graphs, a closely related task. We show that GNNs can outperform spectral methods on sparse graphs, and illustrate these results with numerical examples on both synthetic and real graphs.
