Probabilistic Nested Homogeneous Spaces for Dimensionality Reduction

Xiran Fan, Baba C. Vemuri
Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, PMLR 282:1033-1047, 2026.

Abstract

Dimensionality reduction is a key ingredient of many machine learning algorithms and is paramount to their success. For manifold-valued data, the nonlinear equivalent of the well-known principal component analysis (PCA), called, principal geodesic analysis (PGA) is used quite often. An alternative to PGA that is more general and flexible, called "Nested Homogeneous Spaces (NHS)" for dimensionality reduction of manifold-valued data was recently introduced. In this paper, we present a novel probabilistic version of the NHS model (PNHS) for dimensionality reduction of high dimensional manifold-valued data in Riemannian homogeneous spaces. The PNHS model has several advantages over its deterministic counterpart namely, the NHS model. In particular, the ability to, quantify uncertainty in parameter estimates and tackle missing data. We demonstrate these advantages via real and synthetic data examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v282-fan26a, title = {Probabilistic Nested Homogeneous Spaces for Dimensionality Reduction}, author = {Fan, Xiran and Vemuri, Baba C.}, booktitle = {Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations}, pages = {1033--1047}, year = {2026}, editor = {Acosta, Francisco and Azeglio, Simone and Tolooshams, Bahareh and van de Geijn, Chase and Shewmake, Christian and Sanborn, Sophia and Miolane, Nina}, volume = {282}, series = {Proceedings of Machine Learning Research}, month = {14 Dec 2024--07 Dec 2025}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v282/main/assets/fan26a/fan26a.pdf}, url = {https://proceedings.mlr.press/v282/fan26a.html}, abstract = {Dimensionality reduction is a key ingredient of many machine learning algorithms and is paramount to their success. For manifold-valued data, the nonlinear equivalent of the well-known principal component analysis (PCA), called, principal geodesic analysis (PGA) is used quite often. An alternative to PGA that is more general and flexible, called "Nested Homogeneous Spaces (NHS)" for dimensionality reduction of manifold-valued data was recently introduced. In this paper, we present a novel probabilistic version of the NHS model (PNHS) for dimensionality reduction of high dimensional manifold-valued data in Riemannian homogeneous spaces. The PNHS model has several advantages over its deterministic counterpart namely, the NHS model. In particular, the ability to, quantify uncertainty in parameter estimates and tackle missing data. We demonstrate these advantages via real and synthetic data examples.} }
Endnote
%0 Conference Paper %T Probabilistic Nested Homogeneous Spaces for Dimensionality Reduction %A Xiran Fan %A Baba C. Vemuri %B Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2026 %E Francisco Acosta %E Simone Azeglio %E Bahareh Tolooshams %E Chase van de Geijn %E Christian Shewmake %E Sophia Sanborn %E Nina Miolane %F pmlr-v282-fan26a %I PMLR %P 1033--1047 %U https://proceedings.mlr.press/v282/fan26a.html %V 282 %X Dimensionality reduction is a key ingredient of many machine learning algorithms and is paramount to their success. For manifold-valued data, the nonlinear equivalent of the well-known principal component analysis (PCA), called, principal geodesic analysis (PGA) is used quite often. An alternative to PGA that is more general and flexible, called "Nested Homogeneous Spaces (NHS)" for dimensionality reduction of manifold-valued data was recently introduced. In this paper, we present a novel probabilistic version of the NHS model (PNHS) for dimensionality reduction of high dimensional manifold-valued data in Riemannian homogeneous spaces. The PNHS model has several advantages over its deterministic counterpart namely, the NHS model. In particular, the ability to, quantify uncertainty in parameter estimates and tackle missing data. We demonstrate these advantages via real and synthetic data examples.
APA
Fan, X. & Vemuri, B.C.. (2026). Probabilistic Nested Homogeneous Spaces for Dimensionality Reduction. Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 282:1033-1047 Available from https://proceedings.mlr.press/v282/fan26a.html.

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