用图拉普拉斯矩阵的费德勒值预测GCN性能，揭示结构相似性与模型表现的关系。
Predicting the Performance of Graph Convolutional Networks with Spectral Properties of the Graph Laplacian
- 通过图拉普拉斯矩阵的费德勒值衡量图结构特性
- 费德勒值相近的图在GCN上表现相似，可预测性能
- 适用于图结构分析、模型调参及跨图迁移学习
图卷积网络（GCN）中堆叠层数对节点分类和边预测任务的性能提升并不稳定。我们发现，图的代数连通性（即费德勒值）是预测GCN性能的良好指标。直观上，费德勒值相近的图具有类似结构特征，意味着相同滤波器与超参数在这些图上可能产生相似结果，且跨图迁移学习更有效。我们在合成数据和真实数据集（包括Cora、CiteSeer、Polblogs）上进行理论与实证研究，探索了如何聚合连通分量的费德勒值以得到整体图的值，并证明其可有效预测GCN性能。同时提供了理论解释，说明为何费德勒值具备良好预测能力。
原文摘要 · Abstract (English)
A common observation in the Graph Convolutional Network (GCN) literature is that stacking GCN layers may or may not result in better performance on tasks like node classification and edge prediction. We have found empirically that a graph's algebraic connectivity, which is known as the Fiedler value, is a good predictor of GCN performance. Intuitively, graphs with similar Fiedler values have analogous structural properties, suggesting that the same filters and hyperparameters may yield similar results when used with GCNs, and that transfer learning may be more effective between graphs with similar algebraic connectivity. We explore this theoretically and empirically with experiments on synthetic and real graph data, including the Cora, CiteSeer and Polblogs datasets. We explore multiple ways of aggregating the Fiedler value for connected components in the graphs to arrive at a value for the entire graph, and show that it can be used to predict GCN performance. We also present theoretical arguments as to why the Fiedler value is a good predictor.
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