Learning discriminative node representations benefits various downstream tasks in graph analysis such as community detection and node classification. Existing graph representation learning methods (e.g., based on random walk and contrastive learning) are limited to maximizing the local similarity of connected nodes. Such pair-wise learning schemes could fail to capture the global distribution of representations, since it has no explicit constraints on the global geometric properties of representation space. To this end, we propose Geometric Graph Representation Learning (G2R) to learn node representations in an unsupervised manner via maximizing rate reduction. In this way, G2R maps nodes in distinct groups (implicitly stored in the adjacency matrix) into different subspaces, while each subspace is compact and different subspaces are dispersedly distributed. G2R adopts a graph neural network as the encoder and maximizes the rate reduction with the adjacency matrix. Furthermore, we theoretically and empirically demonstrate that rate reduction maximization is equivalent to maximizing the principal angles between different subspaces. Experiments on real-world datasets show that G2R outperforms various baselines on node classification and community detection tasks.

提出了一种基于几何的无监督图表示学习方法（G2R），它将节点映射到不同的子空间中，并通过最大程度地减小速率来进行优化，并在各种基准测试中表现出优异的节点分类和社区检测任务性能。

通过最大化速率减小实现几何图表示学习