Graph Geometry Interaction Learning
This addresses the challenge of capturing rich geometric properties in graphs for machine learning applications, representing an incremental improvement over existing single-geometry approaches.
The paper tackles the problem of graph embedding by developing a Geometry Interaction Learning (GIL) method that combines Euclidean and hyperbolic geometries to better model complex graph structures, achieving promising results on node classification and link prediction tasks across five benchmark datasets.
While numerous approaches have been developed to embed graphs into either Euclidean or hyperbolic spaces, they do not fully utilize the information available in graphs, or lack the flexibility to model intrinsic complex graph geometry. To utilize the strength of both Euclidean and hyperbolic geometries, we develop a novel Geometry Interaction Learning (GIL) method for graphs, a well-suited and efficient alternative for learning abundant geometric properties in graph. GIL captures a more informative internal structural features with low dimensions while maintaining conformal invariance of each space. Furthermore, our method endows each node the freedom to determine the importance of each geometry space via a flexible dual feature interaction learning and probability assembling mechanism. Promising experimental results are presented for five benchmark datasets on node classification and link prediction tasks.