Search Results for author: Nikolas Schonsheck

Found 3 papers, 1 papers with code

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

1 code implementation19 Sep 2023 Andrew Lee, Harlin Lee, Jose A. Perea, Nikolas Schonsheck, Madeleine Weinstein

Then, we define a continuous and $O(k)$-equivariant map $\pi_\alpha$ that acts as a ``closest point operator'' to project the data onto the image of $V_k(\mathbb{R}^n)$ in $V_k(\mathbb{R}^N)$ under the embedding determined by $\alpha$, while minimizing distortion.

Dimensionality Reduction

Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction

no code implementations14 Dec 2022 Luis Scoccola, Hitesh Gakhar, Johnathan Bush, Nikolas Schonsheck, Tatum Rask, Ling Zhou, Jose A. Perea

The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Johansson takes as input a dataset together with a cohomology class representing a $1$-dimensional hole in the data; the output is a map from the data into the circle that captures this hole, and that is of minimum energy in a suitable sense.

On the chromatic localization of the homotopy completion tower for $\mathcal{O}$-algebras

no code implementations18 Dec 2020 Crichton Ogle, Nikolas Schonsheck

The completion tower of a nonunital commutative ring is a classical construction in commutative algebra.

Algebraic Topology 55P43, 55P48, 55P60, 55U35, 18G55

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