[论文解读] Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily

Tao Wang, Rui Wang+3 more|arXiv (Cornell University)|Dec 27, 2021

Advanced Graph Neural Networks被引用 5

一句话总结

该论文提出HOG-GCN，一种具有自适应传播机制的图卷积网络，其根据节点对之间学习到的同质度动态调整。通过联合从拓扑结构和节点属性中学习同质度，该模型在同质性和异质性图上均提升了性能，在低同质度数据集上超越了最先进方法，同时在同质性图上也保持了具有竞争力的结果。

ABSTRACT

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

研究动机与目标

• 为解决GCN假设强同质性而导致在存在异质性的现实网络中失效的局限性。
• 克服现有异质性感知GNN中高阶邻域聚合引入的噪声和无关信息。
• 设计一种根据节点对之间同质度水平自适应调整的传播机制，而非依赖固定假设。
• 实现同质度估计与特征传播的端到端联合训练，以提升泛化能力。
• 从理论上证明模型根据同质度约束表示相似性。

提出的方法

• 引入可学习的同质度矩阵，利用拓扑和属性信息捕捉节点对之间的同质性/异质性。
• 通过节点特征和图结构得到的类别感知表示来估计同质度，结合可学习权重α和β。
• 将同质度矩阵融入图卷积框架，以调节消息传递与聚合过程。
• 在k阶邻域内采用广义标签传播与同质度引导的特征传播机制，以平衡感受野与噪声。
• 以端到端方式联合训练同质度估计与特征传播。
• 理论分析证明，该模型根据同质度约束表示相似性，从而在同质性和异质性设置下实现更好的类别判别能力。

实验结果

研究问题

• RQ1 图卷积网络能否动态自适应其传播机制以同时处理同质性和异质性图结构？
• RQ2 如何从拓扑和节点属性中有效学习节点对之间的同质度以指导特征传播？
• RQ3 结合属性与拓扑信息是否能提升GNN在低同质度环境下的鲁棒性与性能？
• RQ4 该模型能否避免高阶邻域聚合带来的噪声，同时仍能在异质性网络中捕获足够的类内信息？
• RQ5 所提出的自适应机制在控制基于同质度的表示相似性方面是否具有理论依据？

主要发现

• 在异质性图如Texas和Cornell上，当使用k=2邻域时，HOG-GCN取得显著性能提升，优于k=1和更高k值的结果。
• 在同质性图如Cora和Citeseer上，k=2时性能保持稳定或略有提升，但k值更高时性能下降，表明直接邻域已足够，而高阶聚合会引入噪声。
• 在Texas数据集上，最优的属性与拓扑权重组合（α=0.4，β=0.6）取得最佳性能，证明了融合两种信息源的重要性。
• 学习到的同质度矩阵成功为同质性边分配更高权重，为异质性边分配更低权重，证实了其自适应行为。
• 在所有七个真实世界数据集中，HOG-GCN在异质性或低同质度设置下均优于最先进方法，同时在强同质性设置下也保持了具有竞争力的性能。
• 理论分析确认，该模型根据同质度约束表示相似性，从而在同质性和异质性设置下均实现更好的类别判别能力。