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Authors: Huanran Li 1 and Daniel Pimentel-Alarcón 2

Affiliations: 1 Department of Electrical Engineering, Wisconsin Institute for Discovery University of Wisconsin-Madison, U.S.A. ; 2 Department of Biostatistics, Wisconsin Institute for Discovery University of Wisconsin-Madison, U.S.A.

Keyword(s): Grassmannian, Manifold Learning, Poincare Disk, t-SNE, High-Dimensional Data, Dimensionality Reduction.

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.

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Paper citation in several formats:
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) - IVAPP; ISBN 978-989-758-634-7; ISSN 2184-4321, SciTePress, pages 27-39. DOI: 10.5220/0011609400003417

@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) - IVAPP},
year={2023},
pages={27-39},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011609400003417},
isbn={978-989-758-634-7},
issn={2184-4321},
}

TY - CONF

JO - Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - IVAPP
TI - Visualizing Grassmannians via Poincare Embeddings
SN - 978-989-758-634-7
IS - 2184-4321
AU - Li, H.
AU - Pimentel-Alarcón, D.
PY - 2023
SP - 27
EP - 39
DO - 10.5220/0011609400003417
PB - SciTePress

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