6 papers
Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions
Willem Diepeveen, Deanna Needell
Classical archetypal analysis is appealing for its interpretability, but its linear geometry can limit performance on data with strongly non-linear structure; at the same time, exi…
Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Data
Willem Diepeveen, Oscar Leong
Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, howe…
Iso-Riemannian Optimization on Learned Data Manifolds
Willem Diepeveen, Melanie Weber
We develop a theory of iso-Riemannian optimization for problems constrained to learned data manifolds, a setting in which classical Riemannian optimization - and Riemannian gradien…
Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry
Willem Diepeveen, Deanna Needell
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis…
Curvature Corrected Nonnegative Manifold Data Factorization
Joyce Chew, Willem Diepeveen, Deanna Needell
Data with underlying nonlinear structure are collected across numerous application domains, necessitating new data processing and analysis methods adapted to nonlinear domain struc…
Pulling back symmetric Riemannian geometry for data analysis
Willem Diepeveen
Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Ri…