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.

我们提出一种新颖的鲁棒图结构学习方法，从异质数据中构建高质量的图，进而应用于下游任务。我们首先使用高通滤波器对每个节点进行编码，使其与邻居节点更具有区分度，然后学习一个具有自适应范数的鲁棒图，进一步利用新颖的正则化方法来改进图的结构。对异质图的聚类和半监督分类实验证明了我们方法的有效性。

异质性下的鲁棒图结构学习