Hermitian Symmetric Spaces for Graph Embeddings. (arXiv:2105.05275v1 [cs.LG])

Learning faithful graph representations as sets of vertex embeddings has
become a fundamental intermediary step in a wide range of machine learning
applications. The quality of the embeddings is usually determined by how well
the geometry of the target space matches the structure of the data. In this
work we learn continuous representations of graphs in spaces of symmetric
matrices over C. These spaces offer a rich geometry that simultaneously admits
hyperbolic and Euclidean subspaces, and are amenable to analysis and explicit
computations. We implement an efficient method to learn embeddings and compute
distances, and develop the tools to operate with such spaces. The proposed
models are able to automatically adapt to very dissimilar arrangements without
any apriori estimates of graph features. On various datasets with very diverse
structural properties and reconstruction measures our model ties the results of
competitive baselines for geometrically pure graphs and outperforms them for
graphs with mixed geometric features, showcasing the versatility of our
approach.