5 papers
Simultaneous Optimization of Geodesics and Fréchet Means
Frederik Möbius Rygaard, Søren Hauberg, Steen Markvorsen
A central part of geometric statistics is to compute the Fréchet mean. This is a well-known intrinsic mean on a Riemannian manifold that minimizes the sum of squared Riemannian dis…
A Likely Geometry of Generative Models
Frederik Möbius Rygaard, Shen Zhu, Yinzhu Jin +2
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry witho…
Time-dependent Zermelo navigation with tacking
Steen Markvorsen, Enrique Pendás-Recondo, Frederik Möbius Rygaard
We address the time- and position-dependent Zermelo navigation problem within the framework of Lorentz-Finsler geometry. Since the initial work of E. Zermelo, the task is to find t…
GEORCE: A Fast New Control Algorithm for Computing Geodesics
Frederik Möbius Rygaard, Søren Hauberg
Computing geodesics for Riemannian manifolds is a difficult task that often relies on numerical approximations. However, these approximations tend to be either numerically unstable…
Score Matching Riemannian Diffusion Means
Frederik Möbius Rygaard, Steen Markvorsen, Søren Hauberg +1
Estimating means on Riemannian manifolds is generally computationally expensive because the Riemannian distance function is not known in closed-form for most manifolds. To overcome…