The authors formulate geodesic PCA in Wasserstein space through Otto's fiber bundle, solve it exactly for Gaussians, and approximate it for general measures with neural geodesic parameterizations.
An introduction to optimization on smooth manifolds
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On the Wasserstein Geodesic Principal Component Analysis of probability measures
The authors formulate geodesic PCA in Wasserstein space through Otto's fiber bundle, solve it exactly for Gaussians, and approximate it for general measures with neural geodesic parameterizations.