# Subspace Detours: Building Transport Plans that are Optimal on Subspace Projections

@inproceedings{Muzellec2019SubspaceDB, title={Subspace Detours: Building Transport Plans that are Optimal on Subspace Projections}, author={Boris Muzellec and Marco Cuturi}, booktitle={NeurIPS}, year={2019} }

Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of sliced Wasserstein distances), solve the OT problem between these reduced measures, and settle for the Wasserstein distance between these reductions, rather than that between the original measures. This approach is however difficult to extend to the case in which… Expand

#### 15 Citations

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