<ul><li>This paper discusses the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures.</li><li>The focus is on building submanifolds in the absolute continuous probability measure space, using the Wasserstein-2 distance as the metric.</li><li>These submanifolds allow for local linearizations, similar to Riemannian submanifolds of Euclidean space.</li><li>The paper also presents methods for learning the latent manifold structure and recovering tangent spaces using pairwise extrinsic Wasserstein distances and spectral analysis.</li></ul>

Manifold learning in Wasserstein space

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