Resurrecting Label Propagation for Graphs with Heterophily and Label Noise

Label noise is a common challenge in large datasets, as it can significantly degrade the generalization ability of deep neural networks. Most existing studies focus on noisy labels in computer vision; however, graph models encompass both node features and graph topology as input, and become more susceptible to label noise through message-passing mechanisms. Recently, only a few works have been proposed to tackle the label noise on graphs. One significant limitation is that they operate under the assumption that the graph exhibits homophily and that the labels are distributed smoothly. However, real-world graphs can exhibit varying degrees of heterophily, or even be dominated by heterophily, which results in the inadequacy of the current methods. In this paper, we study graph label noise in the context of arbitrary heterophily, with the aim of rectifying noisy labels and assigning labels to previously unlabeled nodes. We begin by conducting two empirical analyses to explore the impact of graph homophily on graph label noise. Following observations, we propose a efficient algorithm, denoted as $R^{2}LP$. Specifically, $R^{2}LP$ is an iterative algorithm with three steps: (1) reconstruct the graph to recover the homophily property, (2) utilize label propagation to rectify the noisy labels, (3) select high-confidence labels to retain for the next iteration. By iterating these steps, we obtain a set of correct labels, ultimately achieving high accuracy in the node classification task. The theoretical analysis is also provided to demonstrate its remarkable denoising effect. Finally, we perform experiments on ten benchmark datasets with different levels of graph heterophily and various types of noise. In these experiments, we compare the performance of $R^{2}LP$ against ten typical baseline methods. Our results illustrate the superior performance of the proposed $R^{2}LP$.