Graph contrastive learning attracts/disperses node representations for similar/dissimilar node pairs under some notion of similarity. It may be combined with a low-dimensional embedding of nodes to preserve intrinsic and structural properties of a graph. In this paper, we extend the celebrated Laplacian Eigenmaps with contrastive learning, and call them COntrastive Laplacian EigenmapS (COLES). Starting from a GAN-inspired contrastive formulation, we show that the Jensen-Shannon divergence underlying many contrastive graph embedding models fails under disjoint positive and negative distributions, which may naturally emerge during sampling in the contrastive setting. In contrast, we demonstrate analytically that COLES essentially minimizes a surrogate of Wasserstein distance, which is known to cope well under disjoint distributions. Moreover, we show that the loss of COLES belongs to the family of so-called block-contrastive losses, previously shown to be superior compared to pair-wise losses typically used by contrastive methods. We show on popular benchmarks/backbones that COLES offers favourable accuracy/scalability compared to DeepWalk, GCN, Graph2Gauss, DGI and GRACE baselines.

该论文通过引入对比学习方法延伸了Laplacian Eigenmaps，称之为COntrastive Laplacian EigenmapS (COLES)，并证明了COLES基本上最小化了Wasserstein距离的代理，COLES的损失属于所谓的块对比损失中的一种， 相对于DeepWalk，GCN，Graph2Gauss，DGI和GRACE基线模型，COLES在常见基准测试/骨干网络上具有更好的准确性/可扩展性。

对比拉普拉斯特征映射