By exploiting the graph attention network, the authors of this study learn robust node representations of graphs in hyperbolic spaces, utilizing the gyrovector space framework to learn the graph representations in hyperbolic spaces.
In this article, the authors 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, the authors utilize this framework to learn the graph representations in hyperbolic spaces. Specifically, the researchers first use the operations defined in the framework to transform the features in a graph; and they exploit the proximity in the product of hyperbolic spaces to model the multi-head attention mechanism in the non-Euclidean setting; afterward, they further devise a parallel strategy using logarithmic and exponential maps to improve the efficiency of the proposed model. The comprehensive experimental results demonstrate the effectiveness of the proposed model, compared with state-of-the-art methods. Although there is growing research on generalizing graph neural networks (GNNs) to non-Euclidean surfaces, the works in these fields are still scarce. 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. (Published Abstract Provided)