On a linear Gromov-Wasserstein distance

Florian Beier; Robert Beinert; Gabriele Steidl

doi:10.1109/tip.2022.3221286

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arXiv · 2112.11964

On a linear Gromov-Wasserstein distance

Florian Beier·Robert Beinert·Gabriele Steidl

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Abstract

Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal transport (LOT), was successfully used in practice, there does not exist a notion of linear Gromov-Wasserstein distances so far. In this paper, we propose a definition of linear Gromov-Wasserstein distances. We motivate our approach by a generalized LOT model, which is based on barycentric projection maps of transport plans. Numerical examples illustrate that the linear Gromov-Wasserstein distances, similarly as LOT, can replace the expensive computation of pairwise Gromov-Wasserstein distances in applications like shape classification.

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Florian Beier, Robert Beinert, Gabriele Steidl. 2021-12-22. On a linear Gromov-Wasserstein distance. https://doi.org/10.1109/tip.2022.3221286

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