Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real data is inevitably noisy and sparse, which will lead to inferior results. Despite the remarkable success of recent graph representation learning methods, they inherently presume that the graph is homophilic, and largely overlook heterophily, where most connected nodes are from different classes. In this regard, we propose a novel robust graph structure learning method to achieve a high-quality graph from heterophilic data for downstream tasks. We first apply a high-pass filter to make each node more distinctive from its neighbors by encoding structure information into the node features. Then, we learn a robust graph with an adaptive norm characterizing different levels of noise. Afterwards, we propose a novel regularizer to further refine the graph structure. Clustering and semi-supervised classification experiments on heterophilic graphs verify the effectiveness of our method.

翻译：图是描述不同对象之间关系的基本数学结构，已广泛应用于各类学习任务中。大多数方法隐式假设给定图是准确且完整的。然而，真实数据不可避免地带有噪声和稀疏性，这会导致结果性能下降。尽管近期图表示学习方法取得了显著成功，但它们本质上假设图是同质的，而在大多数相连节点来自不同类别的异质性场景中往往被忽视。为此，我们提出了一种新颖的鲁棒图结构学习方法，旨在从异质性数据中为下游任务获取高质量的图。我们首先应用高通滤波器，通过将结构信息编码到节点特征中，使每个节点与其邻居更具区分性。然后，我们使用自适应范数来刻画不同噪声水平，从而学习鲁棒的图结构。随后，我们提出一种新颖的正则化项以进一步优化图结构。在异质性图上的聚类和半监督分类实验验证了我们方法的有效性。