Geometric Graph Representation Learning via Maximizing Rate Reduction

TL;DR

This paper introduces G2R, a novel unsupervised graph representation learning method that maximizes rate reduction to capture global geometric properties, leading to improved performance in node classification and community detection.

Contribution

G2R is the first to apply rate reduction maximization to graph learning, explicitly encouraging global geometric separation of node representations.

Findings

G2R outperforms baselines on node classification tasks.

G2R improves community detection accuracy.

Rate reduction correlates with maximizing principal angles between subspaces.

Abstract

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.