Article ; Online: On a Linear Gromov-Wasserstein Distance.
IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
2022 Volume 31, Page(s) 7292–7305
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 ... ...
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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Language | English |
Publishing date | 2022-11-23 |
Publishing country | United States |
Document type | Journal Article |
ISSN | 1941-0042 |
ISSN (online) | 1941-0042 |
DOI | 10.1109/TIP.2022.3221286 |
Database | MEDical Literature Analysis and Retrieval System OnLINE |
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