Squared Wasserstein, Gromov-Wasserstein, and Fused Gromov-Wasserstein distances decompose into a deterministic linear-optimal-transport component plus a residual, enabling a percentage-of-variance-explained diagnostic for LOT embeddings.
Barycenters in the Wasserstein space
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Fused Gromov-Wasserstein Variance Decomposition with Linear Optimal Transport
Squared Wasserstein, Gromov-Wasserstein, and Fused Gromov-Wasserstein distances decompose into a deterministic linear-optimal-transport component plus a residual, enabling a percentage-of-variance-explained diagnostic for LOT embeddings.