Product Manifold Learning with Independent Coordinate Selection

Jesse He, Tristan Brugère, Gal Mishne
Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), PMLR 221:267-277, 2023.

Abstract

In many dimensionality reduction tasks, we wish to identify the constituent components that explain our observations. For manifold learning, this can be formalized as factoring a Riemannian product manifold. Recovering this factorization, however, may suffer from certain difficulties in practice, especially when data is sparse or noisy, or when one factor is distorted by the other. To address these limitations, we propose identifying non-redundant coordinates on the product manifold before applying product manifold learning to identify which coordinates correspond to different factor manifolds. We demonstrate our approach on both synthetic and real-world data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v221-he23a, title = {Product Manifold Learning with Independent Coordinate Selection}, author = {He, Jesse and Brug\`ere, Tristan and Mishne, Gal}, booktitle = {Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML)}, pages = {267--277}, year = {2023}, editor = {Doster, Timothy and Emerson, Tegan and Kvinge, Henry and Miolane, Nina and Papillon, Mathilde and Rieck, Bastian and Sanborn, Sophia}, volume = {221}, series = {Proceedings of Machine Learning Research}, month = {28 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v221/he23a/he23a.pdf}, url = {https://proceedings.mlr.press/v221/he23a.html}, abstract = {In many dimensionality reduction tasks, we wish to identify the constituent components that explain our observations. For manifold learning, this can be formalized as factoring a Riemannian product manifold. Recovering this factorization, however, may suffer from certain difficulties in practice, especially when data is sparse or noisy, or when one factor is distorted by the other. To address these limitations, we propose identifying non-redundant coordinates on the product manifold before applying product manifold learning to identify which coordinates correspond to different factor manifolds. We demonstrate our approach on both synthetic and real-world data.} }
Endnote
%0 Conference Paper %T Product Manifold Learning with Independent Coordinate Selection %A Jesse He %A Tristan Brugère %A Gal Mishne %B Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML) %C Proceedings of Machine Learning Research %D 2023 %E Timothy Doster %E Tegan Emerson %E Henry Kvinge %E Nina Miolane %E Mathilde Papillon %E Bastian Rieck %E Sophia Sanborn %F pmlr-v221-he23a %I PMLR %P 267--277 %U https://proceedings.mlr.press/v221/he23a.html %V 221 %X In many dimensionality reduction tasks, we wish to identify the constituent components that explain our observations. For manifold learning, this can be formalized as factoring a Riemannian product manifold. Recovering this factorization, however, may suffer from certain difficulties in practice, especially when data is sparse or noisy, or when one factor is distorted by the other. To address these limitations, we propose identifying non-redundant coordinates on the product manifold before applying product manifold learning to identify which coordinates correspond to different factor manifolds. We demonstrate our approach on both synthetic and real-world data.
APA
He, J., Brugère, T. & Mishne, G.. (2023). Product Manifold Learning with Independent Coordinate Selection. Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), in Proceedings of Machine Learning Research 221:267-277 Available from https://proceedings.mlr.press/v221/he23a.html.

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