We introduce a randomized topological augmentor based on Schur complements
for Graph Contrastive Learning (GCL). Given a graph laplacian matrix, the
technique generates unbiased approximations of its Schur complements and treats
the corresponding graphs as augmented views. We discuss the benefits of our
approach, provide theoretical justifications and present connections with graph
diffusion. Unlike previous efforts, we study the empirical effectiveness of the
augmentor in a controlled fashion by varying the design choices for subsequent
GCL phases, such as encoding and contrasting. Extensive experiments on node and
graph classification benchmarks demonstrate that our technique consistently
outperforms pre-defined and adaptive augmentation approaches to achieve
state-of-the-art results.

本文介绍了一种基于 Schur 补的随机拓扑增强器，用于图对比学习，通过生成无偏的 Schur 补近似值，提出了一种有效的图像增强方法，实验结果表明该方法在节点分类和图分类任务中达到了最先进的效果。

用于图对比学习的随机舒尔补视图

Randomized Schur Complement Views for Graph Contrastive Learning

Graph embeddings are a ubiquitous tool for machine learning tasks, such as
node classification and link prediction, on graph-structured data. However,
computing the embeddings for large-scale graphs is prohibitively inefficient
even if we are interested only in a small subset of relevant vertices. To
address this, we present an efficient graph coarsening approach, based on Schur
complements, for computing the embedding of the relevant vertices. We prove
that these embeddings are preserved exactly by the Schur complement graph that
is obtained via Gaussian elimination on the non-relevant vertices. As computing
Schur complements is expensive, we give a nearly-linear time algorithm that
generates a coarsened graph on the relevant vertices that provably matches the
Schur complement in expectation in each iteration. Our experiments involving
prediction tasks on graphs demonstrate that computing embeddings on the
coarsened graph, rather than the entire graph, leads to significant time
savings without sacrificing accuracy.

对于大规模图形数据，我们提出了一种优化的图粗化方法，基于 Schur 补，可在节省时间的同时保证了嵌入的准确性。