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Pré-Publication, Document De Travail Année : 2022

Spherical Sliced-Wasserstein

Résumé

Many variants of the Wasserstein distance have been introduced to reduce its original computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages one-dimensional projections for which a closed-form solution of the Wasserstein distance is available, has received a lot of interest. Yet, it is restricted to data living in Euclidean spaces, while the Wasserstein distance has been studied and used recently on manifolds. We focus more specifically on the sphere, for which we define a novel SW discrepancy, which we call spherical Sliced-Wasserstein, making a first step towards defining SW discrepancies on manifolds. Our construction is notably based on closed-form solutions of the Wasserstein distance on the circle, together with a new spherical Radon transform. Along with efficient algorithms and the corresponding implementations, we illustrate its properties in several machine learning use cases where spherical representations of data are at stake: density estimation on the sphere, variational inference or hyperspherical auto-encoders.

Dates et versions

hal-03852488 , version 1 (15-11-2022)

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Citer

Clément Bonet, Paul Berg, Nicolas Courty, François Septier, Lucas Drumetz, et al.. Spherical Sliced-Wasserstein. 2022. ⟨hal-03852488⟩
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