Combinatorics

Graph

Euclidean space

Pure mathematics

Voltage graph

Mathematics

Logarithm

Hyperbolic space

Euclidean geometry

World Wide Web

Mathematical analysis

Exploit

Hyperbolic geometry

Line graph

Geometry

Random geometric graph

Computer science

Geometric networks

Algebraic geometry

Theoretical computer science

Complex network

Computer security

Algebraic number

IEEE Transactions on Big Data

Graph neural network (GNN) has shown superior performance in dealing with structured graphs, which has attracted considerable research attention recently. Most of the existing GNNs are designed in Euclidean spaces; however, real-world spatial structured data can be non-Euclidean surfaces (e.g., hyperbolic spaces). For example, biologists may inspect the geometric shape of a protein surface to determine its interaction with other biomolecules for drug discovery. Although there is growing research on generalizing GNNs to non-Euclidean surfaces, the works in these fields are still scarce. In this paper, we exploit the graph attention network to learn robust node representations of graphs in hyperbolic spaces. As the gyrovector space framework provides an elegant algebraic formalism for hyperbolic geometry, we utilize this framework to learn the graph representations in hyperbolic spaces. Specifically, we first use the operations defined in the framework to transform the features in a graph; and we exploit the proximity in the product of hyperbolic spaces to model the multi-head attention mechanism in the non-Euclidean setting; afterward, we further devise a parallel strategy using logarithmic and exponential maps to improve the efficiency of our proposed model. The comprehensive experimental results demonstrate the effectiveness of the proposed model, compared with state-of-the-art methods.

Hyperbolic Graph Attention Network