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Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicing
Clément Bonet, Elsa Cazelles, Lucas Drumetz +1
The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian man…
Bridging Arbitrary and Tree Metrics via Differentiable Gromov Hyperbolicity
Pierre Houedry, Nicolas Courty, Florestan Martin-Baillon +2
Trees and the associated shortest-path tree metrics provide a powerful framework for representing hierarchical and combinatorial structures in data. Given an arbitrary metric space…
Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds
Clément Bonet, Lucas Drumetz, Nicolas Courty
While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such sp…