Nikolas Schonsheck

collaborators

3 papers

math.AT2025

Dowker's theorem for higher-order relations

Vin de Silva, Chad Giusti, Vladimir Itskov +5

Given a relation $R \subseteq I \times J$ between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker comp…

math.AT2025

Spherical Coordinates from Persistent Cohomology

Nikolas C. Schonsheck, Stefan C. Schonsheck

We describe a method to obtain spherical parameterizations of arbitrary data through the use of persistent cohomology and variational optimization. We begin by computing the second…

cs.CG2025

$O (k)$ -Equivariant Dimensionality Reduction on Stiefel Manifolds

Andrew Lee, Harlin Lee, Jose A. Perea +2

Many real-world datasets live on high-dimensional Stiefel and Grassmannian manifolds, $V_{k} (R^{N})$ and $G r (k, R^{N})$ respectively, and benefit from projection onto l…

Dowker's theorem for higher-order relations

Spherical Coordinates from Persistent Cohomology

O(k)-Equivariant Dimensionality Reduction on Stiefel Manifolds

$O (k)$ -Equivariant Dimensionality Reduction on Stiefel Manifolds