Hyperbolic Graph Convolutional Neural Networks

Ines Chami, Rex Ying, Christopher Ré, Jure Leskovec

Abstract: Graph convolutional networks (GCNs) map nodes in a graph to Euclidean embeddings, which have been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers an exciting alternative as it enables embeddings with much smaller distortion. However, extending GCNs to hyperbolic geometry presents several unique challenges: It is not clear how to define neural network operations, such as feature transformation and aggregation, in hyperbolic space. Furthermore since input features are often Euclidean, it is unclear how to transform the features into hyperbolic embeddings with the right amount of curvature. Here we propose Hyperbolic Graph Convolutional Neural Network (HYPERGCN), the first inductive hyperbolic GCNs that leverages both the expressiveness of GCNs and hyperbolic geometry to learn inductive node representations for hierarchical and scale-free graphs. We derive graph convolution operations in the hyperboloid model of hyperbolic space and map Euclidean input features to embeddings in a hyperbolic space with a different trainable curvature at each layer. Experiments demonstrate that HYPERGCN learns embeddings that preserve hierarchical structure, and lead to improved performance when compared to its Euclidean analogs, even with very low dimensional embeddings: compared to state-of-the-art GNNs, HYPERGCN achieves an error reduction up to 63.1% in ROC AUC for link prediction and up to 47.5% in F1 score for node classification, also improving state-of-the art on the Pubmed dataset.

Code Link: https://github.com/HazyResearch/hgcn

CMT Num: 2699