  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.
