Geometric Graph Representation Learning via Maximizing Rate Reduction
This addresses the limitation of existing graph representation learning methods that focus on local similarity, offering a more global approach for tasks like community detection and node classification, though it appears incremental as it builds on existing graph neural network encoders.
The paper tackles the problem of learning discriminative node representations for graph analysis by proposing Geometric Graph Representation Learning (G2R), which uses rate reduction maximization to capture global geometric properties, resulting in improved performance on node classification and community detection tasks over various baselines.
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.