Visualizing Grassmannians via Poincare Embeddings

Huanran Li, Daniel Pimentel-Alarcón

2023

Abstract

This paper introduces an embedding to visualize high-dimensional Grassmannians on the Poincaré disk, obtained by minimizing the KL-divergence of the geodesics on each manifold. Our main theoretical result bounds the loss of our embedding by a log-factor of the number of subspaces, and a term that depends on the distribution of the subspaces in the Grassmannian. This term will be smaller if the subspaces form well-defined clusters, and larger if the subspaces have no structure whatsoever. We complement our theory with synthetic and real data experiments showing that our embedding can provide a more accurate visualization of Grassmannians than existing representations.

Paper Citation

in Harvard Style

Li H. and Pimentel-Alarcón D. (2023). Visualizing Grassmannians via Poincare Embeddings. In Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 3: IVAPP; ISBN 978-989-758-634-7, SciTePress, pages 27-39. DOI: 10.5220/0011609400003417

in Bibtex Style

@conference{ivapp23,
author={Huanran Li and Daniel Pimentel-Alarcón},
title={Visualizing Grassmannians via Poincare Embeddings},
booktitle={Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 3: IVAPP},
year={2023},
pages={27-39},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011609400003417},
isbn={978-989-758-634-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 3: IVAPP
TI - Visualizing Grassmannians via Poincare Embeddings
SN - 978-989-758-634-7
AU - Li H.
AU - Pimentel-Alarcón D.
PY - 2023
SP - 27
EP - 39
DO - 10.5220/0011609400003417
PB - SciTePress