Search Results for author: Caroline Moosmüller

Found 5 papers, 0 papers with code

Point Cloud Classification via Deep Set Linearized Optimal Transport

no code implementations2 Jan 2024 Scott Mahan, Caroline Moosmüller, Alexander Cloninger

Our approach is motivated by the observation that $L^2-$distances between optimal transport maps for distinct point clouds, originating from a shared fixed reference distribution, provide an approximation of the Wasserstein-2 distance between these point clouds, under certain assumptions.

Classification Point Cloud Classification

Manifold learning in Wasserstein space

no code implementations14 Nov 2023 Keaton Hamm, Caroline Moosmüller, Bernhard Schmitzer, Matthew Thorpe

This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures on a compact and convex subset of $\mathbb{R}^d$, metrized with the Wasserstein-2 distance $W$.

Linearized Wasserstein dimensionality reduction with approximation guarantees

no code implementations14 Feb 2023 Alexander Cloninger, Keaton Hamm, Varun Khurana, Caroline Moosmüller

We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space.

Dimensionality Reduction

Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations

no code implementations20 Aug 2020 Caroline Moosmüller, Alexander Cloninger

The transform is defined by computing the optimal transport of each distribution to a fixed reference distribution, and has a number of benefits when it comes to speed of computation and to determining classification boundaries.

General Classification

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