GRAIL: Graph contrastive learning with balanced negative sampling

Currently, some graph contrastive learning methods mitigate the class imbalance by balancing the number of anchors, overlooking the crucial role of negative samples in forming a regular simplex. Moreover, existing strategies select a limited number of positive samples with poor quality, causing the model to erroneously push away nodes with similar semantics. To address these issues, we propose a graph contrastive learning method with balanced negative sampling, named GRAIL. Specifically, GRAIL introduces a multi-head similarity metric that leverages mixed probability distributions related to dimensional elements to adaptively select an equal number of hard negative samples within each non-anchor cluster. As a result, GRAIL not only promotes the formation of a regular simplex by balancing the gradient contributions of different negative classes but also selects the most informative hard negative samples to improve the distinguishing ability of minority classes while minimizing the impact on majority classes. Furthermore, GRAIL selects multiple positive samples with a high correct ratio using structural similarity and feature similarity, thereby enabling the model to learn trustworthy node representations. Since traditional contrastive loss focuses on the majority class while neglecting the minority class, a balanced contrastive loss is introduced to optimize node representations. Experiments on node classification, node clustering, and link prediction tasks across six imbalanced graph datasets demonstrate that GRAIL outperforms existing state-of-the-art methods. The source code is available at https://github.com/xushucheng-coder/GRAIL/tree/master.