Graph-based semi-supervised learning (GSSL) has been used successfully in various applications. Existing methods leverage the graph structure and labeled samples for classification. Label Propagation (LP) and Graph Neural Networks (GNNs) both iteratively pass messages on graphs, where LP propagates node labels through edges and GNN aggregates node features from the neighborhood. Recently, combining LP and GNN has led to improved performance. However, utilizing labels and features jointly in higher-order graphs has not been explored. Therefore, we propose Nonlinear Correct and Smooth (NLCS), which improves the existing post-processing approach by incorporating non-linearity and higher-order representation into the residual propagation to handle intricate node relationships effectively. Systematic evaluations show that our method achieves remarkable average improvements of 13.71% over base prediction and 2.16% over the state-of-the-art post-processing method on six commonly used datasets. Comparisons and analyses show our method effectively utilizes labels and features jointly in higher-order graphs to resolve challenging graph relationships.

翻译：基于图的半监督学习（GSSL）已在各类应用中成功运用。现有方法通过利用图结构和标注样本进行分类。标签传播（LP）与图神经网络（GNN）均在图结构上迭代传递信息，其中LP通过边传播节点标签，而GNN则聚合邻域节点特征。近年来，LP与GNN的结合带来了性能提升。然而，如何在更高阶图中联合利用标签与特征的问题尚未得到充分探索。为此，我们提出非线性纠正与平滑方法（NLCS），该方法通过将非线性和高阶表示引入残差传播过程，有效处理复杂节点关系，从而改进现有后处理技术。系统评估表明，在六个常用数据集上，该方法相较于基础预测平均提升13.71%，相较于当前最优后处理方法平均提升2.16%。对比分析与消融实验证实，该方法能有效在更高阶图中联合利用标签与特征，解决具有挑战性的图关系问题。