Hermitian Symmetric Spaces for Graph Embeddings
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.
Code (1)
Similar Papers 제목 키워드 기반
Complex Embeddings for Simple Link Prediction
In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factoriza…
Link PredictionPredictionRelational ReasoningSymmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in repre…
Graph ReconstructionNode ClassificationRecommendation SystemsRepresentation Learning+1Machine learning for knowledge acquisition and accelerated inverse-design for non-Hermitian systems
Non-Hermitian systems offer new platforms for unusual physical properties that can be flexibly manipulated by redistribution of the real and imaginary parts of refractive indices, whose presence breaks conventional wave …
BIG-bench Machine LearningDeep LearningSkew-Symmetric Adjacency Matrices for Clustering Directed Graphs
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clu…
ClusteringGraph ClusteringRiemannian Gaussian distributions, random matrix ensembles and diffusion kernels
We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functio…