When learning from graph data, the graph and the node features both give noisy information about the node labels. In this paper we propose an algorithm to jointly denoise the features and rewire the graph (JDR), which improves the performance of downstream node classification graph neural nets (GNNs). JDR works by aligning the leading spectral spaces of graph and feature matrices. It approximately solves the associated non-convex optimization problem in a way that handles graphs with multiple classes and different levels of homophily or heterophily. We theoretically justify JDR in a stylized setting and show that it consistently outperforms existing rewiring methods on a wide range of synthetic and real-world node classification tasks.

翻译：当从图数据中学习时，图结构和节点特征均会提供关于节点标签的含噪信息。本文提出一种联合去噪特征与重连图的算法（JDR），该算法可提升下游节点分类图神经网络（GNNs）的性能。JDR通过对齐图矩阵与特征矩阵的主导谱空间实现其功能。该算法以近似求解的方式处理关联的非凸优化问题，能够适应具有多类别及不同同配性或异配性水平的图结构。我们在理论框架下论证了JDR的有效性，并通过大量合成与真实场景的节点分类任务验证了其相较于现有重连方法的持续优越性。