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

TopoGCL: Topological Graph Contrastive Learning

Extended persistence is a technique from topological data analysis to obtain
global multiscale topological information from a graph. This includes
information about connected components and cycles that are captured by the
so-called persistence barcodes. We introduce extended persistence into a
supervised learning framework for graph classification. Global topological
information, in the form of a barcode with four different types of bars and
their explicit cycle representatives, is combined into the model by the readout
function which is computed by extended persistence. The entire model is
end-to-end differentiable. We use a link-cut tree data structure and
parallelism to lower the complexity of computing extended persistence,
obtaining a speedup of more than 60x over the state-of-the-art for extended
persistence computation. This makes extended persistence feasible for machine
learning. We show that, under certain conditions, extended persistence
surpasses both the WL[1] graph isomorphism test and 0-dimensional barcodes in
terms of expressivity because it adds more global (topological) information. In
particular, arbitrarily long cycles can be represented, which is difficult for
finite receptive field message passing graph neural networks. Furthermore, we
show the effectiveness of our method on real world datasets compared to many
existing recent graph representation learning methods.

使用扩展持久性技术将全局拓扑信息融入图分类的监督学习框架中，通过可导的读出函数计算扩展持久性获取全局拓扑信息；使用链剪树数据结构和并行计算降低计算复杂度，使扩展持久性在机器学习中具备可行性。研究结果表明，在特定条件下，扩展持久性在表达能力上超越了 WL 图同构测试和 0 维条形码，因为它提供更多的全局（拓扑）信息，并能表示任意长的循环。此外，通过与现有的图表示学习方法进行比较，验证了我们方法在真实数据集上的有效性。