Nonlinear Correct and Smooth for Graph-Based Semi-Supervised Learning

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Graph-based semi-supervised learning (GSSL) has achieved significant success across various applications by leveraging the graph structure and labeled samples for classification tasks. In the field of GSSL, Label Propagation (LP) and Graph Neural Networks (GNNs) are two complementary methods, in which LP iteratively propagates and updates node labels through connected nodes, whereas GNNs aggregate node features by incorporating information from their neighbors. Recently, the complementary nature of LP and GNNs has been utilized to improve performance through the combination of two approaches. However, the utilization of higher-order graph structures within these combined approaches, such as triangles, is still underexplored. Therefore, to advance understanding in this ongoing research, we first model GSSL as a two-step Feature-Label process. Then, we introduce Nonlinear Correct and Smooth (NLCS) in the post-processing step, a combined method that incorporates nonlinearity and higher-order structures into the residual propagation to handle intricate node relationships effectively. We propose a new synthetic graph generator to deepen the analysis and broaden the experimentation, providing insights into the mechanisms that enable NLCS to handle intricate node relationships effectively. Our systematic evaluations across six synthetic graphs show that NLCS outperforms base predictions by an average of 12.44% and the existing state-of-the-art post-processing method by 8.04%. Furthermore, on six commonly used real-world datasets, NLCS demonstrates a 10.9% improvement over six base prediction models and a 1.6% over the state-of-the-art post-processing method. Our comparisons and analyses reveal that NLCS substantially enhances the prediction accuracy of nodes within complex graph structures by effectively utilizing higher-order structures of graphs.