
SemiRiemannian Graph Convolutional Networks
Graph Convolutional Networks (GCNs) are typically studied through the le...
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Design and visualization of Riemannian metrics
Local and global illumination were recently defined in Riemannian manifo...
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geomstats: a Python Package for Riemannian Geometry in Machine Learning
We introduce geomstats, a python package that performs computations on m...
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Learning Graph Embeddings on ConstantCurvature Manifolds for Change Detection in Graph Streams
The space of graphs is characterized by a nontrivial geometry, which of...
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Hermitian Symmetric Spaces for Graph Embeddings
Learning faithful graph representations as sets of vertex embeddings has...
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Adversarial Autoencoders with ConstantCurvature Latent Manifolds
Constantcurvature Riemannian manifolds (CCMs) have been shown to be ide...
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Learning graphstructured data using Poincaré embeddings and Riemannian Kmeans algorithms
Recent literature has shown several benefits of hyperbolic embedding of ...
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Computationally Tractable Riemannian Manifolds for Graph Embeddings
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic geometry. However, going beyond embedding spaces of constant sectional curvature, while potentially more representationally powerful, proves to be challenging as one can easily lose the appeal of computationally tractable tools such as geodesic distances or Riemannian gradients. Here, we explore computationally efficient matrix manifolds, showcasing how to learn and optimize graph embeddings in these Riemannian spaces. Empirically, we demonstrate consistent improvements over Euclidean geometry while often outperforming hyperbolic and elliptical embeddings based on various metrics that capture different graph properties. Our results serve as new evidence for the benefits of nonEuclidean embeddings in machine learning pipelines.
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