Graph Neural Networks (GNNs) have proven to be powerful in many graph-based applications. However, they fail to generalize well under heterophilic setups, where neighbor nodes have different labels. To address this challenge, we employ a confidence ratio as a hyper-parameter, assuming that some of the edges are disassortative (heterophilic). Here, we propose a two-phased algorithm. Firstly, we determine edge coefficients through subgraph matching using a supplementary module. Then, we apply GNNs with a modified label propagation mechanism to utilize the edge coefficients effectively. Specifically, our supplementary module identifies a certain proportion of task-irrelevant edges based on a given confidence ratio. Using the remaining edges, we employ the widely used optimal transport to measure the similarity between two nodes with their subgraphs. Finally, using the coefficients as supplementary information on GNNs, we improve the label propagation mechanism which can prevent two nodes with smaller weights from being closer. The experiments on benchmark datasets show that our model alleviates over-smoothing and improves performance.

翻译：图神经网络（GNN）已在众多基于图的应用中展现出强大效能。然而，在邻居节点具有不同标签的异亲设置下，它们难以实现良好的泛化。为解决这一挑战，我们采用置信度比作为超参数，假设部分边为失配（异亲）关系。本文提出一种两阶段算法：首先，通过使用辅助模块进行子图匹配来确定边的系数；随后，应用带有改进标签传播机制的GNN来有效利用这些边系数。具体而言，我们的辅助模块基于给定置信度比识别一定比例的任务无关边。利用剩余边，我们采用广泛使用的最优传输方法，通过子图衡量两个节点间的相似度。最后，将这些系数作为GNN的补充信息，改进标签传播机制，从而防止权重较小的两个节点在特征空间中过度接近。在基准数据集上的实验表明，我们的模型能缓解过平滑问题并提升性能。