5 citations · 11 across the 6 of their papers we have counts for
7 papers
Beyond Unimodal Bases: Pullback Geometry for Multimodal Data
Honglei Brinkmann, Lucas Ng, Georgios Batzolis +3
Data-driven Riemannian geometry provides nonlinear interpolation and geometric representations of high-dimensional data. For these operations to be statistically meaningful, paths…
Pullback Flow Matching on Data Manifolds
Friso de Kruiff, Erik Bekkers, Ozan Öktem +2
We propose Pullback Flow Matching (PFM), a novel framework for generative modeling on data manifolds. Unlike existing methods that assume or learn restrictive closed-form manifold…
Score-based Pullback Riemannian Geometry: Extracting the Data Manifold Geometry using Anisotropic Flows
Willem Diepeveen, Georgios Batzolis, Zakhar Shumaylov +1
Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is cr…
Riemannian geometry for efficient analysis of protein dynamics data
Willem Diepeveen, Carlos Esteve-Yagüe, Jan Lellmann +2
An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets shoul…
Spectral decomposition of atomic structures in heterogeneous cryo-EM
Carlos Esteve-Yagüe, Willem Diepeveen, Ozan Öktem +1
We consider the problem of recovering the three-dimensional atomic structure of a flexible macromolecule from a heterogeneous cryo-EM dataset. The dataset contains noisy tomographi…
Regularising orientation estimation in Cryo-EM 3D map refinement through measure-based lifting over Riemannian manifolds
Willem Diepeveen, Jan Lellmann, Ozan Öktem +1
Motivated by the trade-off between noise-robustness and data-consistency for joint 3D map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (C…
An Inexact Semi-smooth Newton Method on Riemannian Manifolds with Application to Duality-based Total Variation Denoising
Willem Diepeveen, Jan Lellmann
We propose a higher-order method for solving non-smooth optimization problems on manifolds. In order to obtain superlinear convergence, we apply a Riemannian Semi-smooth Newton met…