2023/06/24 by Wei Zhao, Federico López, Zhao, Wei +9
Computer Science · #Advanced Graph Neural Networks #FOS: Computer and information sciences #Graph Theory and Algorithms #Machine Learning (cs.LG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2306.14064
openalex publication_date 2023/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces allows for representing graphs with uniform geometric and topological features, such as grids and hierarchies, with minimal distortion. However, real-world graph data is characterized by multiple types of geometric and topological features, necessitating more sophisticated geometric embedding spaces. In this work, we utilize the Riemannian symmetric space of symmetric positive definite matrices (SPD) to construct graph neural networks that can robustly handle complex graphs. To do this, we develop an innovative library that leverages the SPD gyrocalculus tools \citelopez2021gyroSPD to implement the building blocks of five popular graph neural networks in SPD. Experimental results demonstrate that our graph neural networks in SPD substantially outperform their counterparts in Euclidean and hyperbolic spaces, as well as the Cartesian product thereof, on complex graphs for node and graph classification tasks. We release the library and datasets at \urlhttps://github.com/andyweizhao/SPD4GNNs.