Graph contrastive learning (GCL) has recently emerged as a new concept which allows for capitalizing on the strengths of graph neural networks (GNNs) to learn rich representations in a wide variety of applications which involve abundant unlabeled information. However, existing GCL approaches largely tend to overlook the important latent information on higher-order graph substructures. We address this limitation by introducing the concepts of topological invariance and extended persistence on graphs to GCL. In particular, we propose a new contrastive mode which targets topological representations of the two augmented views from the same graph, yielded by extracting latent shape properties of the graph at multiple resolutions. Along with the extended topological layer, we introduce a new extended persistence summary, namely, extended persistence landscapes (EPL) and derive its theoretical stability guarantees. Our extensive numerical results on biological, chemical, and social interaction graphs show that the new Topological Graph Contrastive Learning (TopoGCL) model delivers significant performance gains in unsupervised graph classification for 11 out of 12 considered datasets and also exhibits robustness under noisy scenarios.

图对比学习在图神经网络的强大优势下充分利用丰富的无标签信息来学习图的特征表示，然而现有的方法忽视了高阶图子结构的重要潜在信息，本研究通过引入拓扑不变性和扩展持久性的概念来解决这个限制，提出了一种新的对比学习模式并引入了扩展持久性景观，实验结果表明TopoGCL模型在无监督图分类中取得了显著的性能提升。

TopoGCL: 拓扑图对比学习