Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networks
This addresses the challenge of representing graphs with mixed geometries for machine learning applications, though it appears incremental as it builds on existing graph neural network frameworks.
The paper tackles the problem of sub-optimal graph representation by embedding all nodes in a single Euclidean or hyperbolic space, proposing a method to select node-specific embedding spaces based on local hyperbolicity, resulting in promising performance on node classification and link prediction tasks.
Many graph neural networks have been developed to learn graph representations in either Euclidean or hyperbolic space, with all nodes' representations embedded in a single space. However, a graph can have hyperbolic and Euclidean geometries at different regions of the graph. Thus, it is sub-optimal to indifferently embed an entire graph into a single space. In this paper, we explore and analyze two notions of local hyperbolicity, describing the underlying local geometry: geometric (Gromov) and model-based, to determine the preferred space of embedding for each node. The two hyperbolicities' distributions are aligned using the Wasserstein metric such that the calculated geometric hyperbolicity guides the choice of the learned model hyperbolicity. As such our model Joint Space Graph Neural Network (JSGNN) can leverage both Euclidean and hyperbolic spaces during learning by allowing node-specific geometry space selection. We evaluate our model on both node classification and link prediction tasks and observe promising performance compared to baseline models.