[论文解读] Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks

Yujun Yan, Milad Hashemi+3 more|arXiv (Cornell University)|Feb 12, 2021

Advanced Graph Neural Networks参考文献 43被引用 25

一句话总结

本论文联合用节点层级指标解释GCN中的过平滑和异质性，并提出GGCN，通过基于结构和特征的边缘修正来同时解决这两个问题。

ABSTRACT

In node classification tasks, graph convolutional neural networks (GCNs) have demonstrated competitive performance over traditional methods on diverse graph data. However, it is known that the performance of GCNs degrades with increasing number of layers (oversmoothing problem) and recent studies have also shown that GCNs may perform worse in heterophilous graphs, where neighboring nodes tend to belong to different classes (heterophily problem). These two problems are usually viewed as unrelated, and thus are studied independently, often at the graph filter level from a spectral perspective. We are the first to take a unified perspective to jointly explain the oversmoothing and heterophily problems at the node level. Specifically, we profile the nodes via two quantitative metrics: the relative degree of a node (compared to its neighbors) and the node-level heterophily. Our theory shows that the interplay of these two profiling metrics defines three cases of node behaviors, which explain the oversmoothing and heterophily problems jointly and can predict the performance of GCNs. Based on insights from our theory, we show theoretically and empirically the effectiveness of two strategies: structure-based edge correction, which learns corrected edge weights from structural properties (i.e., degrees), and feature-based edge correction, which learns signed edge weights from node features. Compared to other approaches, which tend to handle well either heterophily or oversmoothing, we show that {our model, GGCN}, which incorporates the two strategies performs well in both problems.

研究动机与目标

• 引入在理论上有依据的节点级指标，以在GCN各层对节点进行画像（相对度和节点级异质性）。
• 基于节点行为对过平滑和异质性问题给出联合解释。
• 开发并验证通过结构和节点特征纠正边的方法，以缓解这两种问题。

提出的方法

• 定义节点级同质性h_i和相对度overline{r_i}来表征跨层节点行为。
• 推导理论条件（Theorems 3.1–3.3）将节点指标与节点表示的变动及错误分类联系起来。
• 提出基于结构的边修正，通过学习层特定的边标量tau_{ij}^l来调节邻居影响。
• 提出基于特征的边修正，通过使用节点表示之间的余弦相似度来学习符号化的边权，以创建正向/负向信息传递路径。
• 引入衰减聚合，以减慢表示收敛并提高稳定性。
• 将GGCN作为一个统一模型，结合两种边修正机制和衰减聚合。

实验结果

研究问题

• RQ1 节点级指标（相对度和节点级同质性）如何解释GCN中的过平滑和异质性？
• RQ2 基于结构和特征的边修正策略是否能同时缓解过平滑和异质性，并且在具有不同同质性水平的数据集上表现如何？
• RQ3 相比现有模型，带符号边和层级修正是否能提高GCN对过平滑和异质性的鲁棒性？

主要发现

• 相对度与节点级同质性的相互作用定义了跨层的三种节点行为，联合解释了过平滑和异质性。
• 符号化边权在特定错误率和度数条件下可以帮助缓解这两个问题。
• 基于结构的边修正利用与度相关的特性来改进边权，防止高同质性图中的过平滑。
• 基于特征的边修正使用基于余弦的符号来区分正向和负向邻居影响，在异质性图中提升性能。
• 所提出的GGCN，结合两种边修正策略和衰减聚合，在高异质性数据集上实现强性能，在同质性数据集上也具有竞争力。