Graph Neural Networks (GNNs) have been widely used to learn node representations and with outstanding performance on various tasks such as node classification. However, noise, which inevitably exists in real-world graph data, would considerably degrade the performance of GNNs revealed by recent studies. In this work, we propose a novel and robust GNN encoder, Low-Rank Graph Contrastive Learning (LR-GCL). Our method performs transductive node classification in two steps. First, a low-rank GCL encoder named LR-GCL is trained by prototypical contrastive learning with low-rank regularization. Next, using the features produced by LR-GCL, a linear transductive classification algorithm is used to classify the unlabeled nodes in the graph. Our LR-GCL is inspired by the low frequency property of the graph data and its labels, and it is also theoretically motivated by our sharp generalization bound for transductive learning. To the best of our knowledge, our theoretical result is among the first to theoretically demonstrate the advantage of low-rank learning in graph contrastive learning supported by strong empirical performance. Extensive experiments on public benchmarks demonstrate the superior performance of LR-GCL and the robustness of the learned node representations. The code of LR-GCL is available at \url{https://anonymous.4open.science/r/Low-Rank_Graph_Contrastive_Learning-64A6/}.

翻译：图神经网络（GNN）已广泛用于学习节点表示，并在节点分类等各类任务中取得了卓越性能。然而，近期研究表明，真实世界图数据中不可避免存在的噪声会显著降低GNN的性能。本文提出一种新颖且鲁棒的GNN编码器——低秩图对比学习（LR-GCL）。该方法通过两步实现直推式节点分类：首先，通过原型对比学习结合低秩正则化训练名为LR-GCL的低秩GCL编码器；随后，利用LR-GCL生成的特征，采用线性直推分类算法对图中未标记节点进行分类。LR-GCL的灵感来源于图数据及其标签的低频特性，并受到我们针对直推学习所提出的严格泛化界限的理论支持。据我们所知，我们的理论结果首次从理论上证明了低秩学习在图对比学习中的优势，且得到了强实验验证支持。在公开基准上的大量实验表明，LR-GCL具有优越性能，且学习到的节点表示具有鲁棒性。LR-GCL代码见\url{https://anonymous.4open.science/r/Low-Rank_Graph_Contrastive_Learning-64A6/}。