11 papers
Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functions
Richard Duong, Viktor Stein, Robert Beinert +2
We give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals towards given target mea…
A Discrete Radon Transform Based on the Area of Cube-Plane Intersection
Robert Beinert, Jonas Bresch, Michael Quellmalz
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an a…
Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport
Moritz Piening, Robert Beinert
Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein over Wass…
Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition
Matthias Beckmann, Robert Beinert, Jonas Bresch
The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely…
A Novel Sliced Fused Gromov-Wasserstein Distance
Moritz Piening, Robert Beinert
The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both dista…
Slicing the Gaussian Mixture Wasserstein Distance
Moritz Piening, Robert Beinert
Gaussian mixture models (GMMs) are widely used in machine learning for tasks such as clustering, classification, image reconstruction, and generative modeling. A key challenge in w…