Dimensionality Reduction on the SPD Manifold: A Comparative Study of Linear and Non-Linear Methods

Amal Araoud, Enjie Ghorbel, Enjie Ghorbel, Faouzi Ghorbel

2025

Abstract

The representation of visual data using Symmetric Positive Definite (SPD) matrices has proven effective in numerous computer vision applications. Nevertheless,the non-Euclidean nature of the SPD space poses a challenge, especially when dealing with high-dimensional data. Conventional dimensionality reduction methods have been typically designed for data lying in linear spaces, rendering them theoretically unsuitable for SPD matrices. For that reason, considerable efforts have been made to adapt these methods to the SPD space by leveraging its Riemannian structure. Despite these advances, a systematic comparison of conventional, i.e., linear and revisited, i.e., non-linear dimensionality reduction methods applied to SPD data according to their distribution remains lacking. In fact, while geometry-aware dimensionality reduction methods are highly relevant, the convexity of the SPD space may hinder their performance. This study addresses this gap by evaluating the performance of both linear and non-linear dimensionality reduction techniques within a binary classification scenario. For that purpose, a synthetically generated dataset exhibiting different class distribution configurations (distant, slight overlap, strong overlap) is used. The obtained results suggest that non-linear methods offer limited advantages over linear approaches. According to our analysis, this outcome may be attributed to two primary factors: the convexity of the SPD space and numerical issues.

Paper Citation

in Harvard Style

Araoud A., Ghorbel E. and Ghorbel F. (2025). Dimensionality Reduction on the SPD Manifold: A Comparative Study of Linear and Non-Linear Methods. In Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART; ISBN 978-989-758-737-5, SciTePress, pages 805-812. DOI: 10.5220/0013183500003890

in Bibtex Style

@conference{icaart25,
author={Amal Araoud and Enjie Ghorbel and Faouzi Ghorbel},
title={Dimensionality Reduction on the SPD Manifold: A Comparative Study of Linear and Non-Linear Methods},
booktitle={Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART},
year={2025},
pages={805-812},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013183500003890},
isbn={978-989-758-737-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART
TI - Dimensionality Reduction on the SPD Manifold: A Comparative Study of Linear and Non-Linear Methods
SN - 978-989-758-737-5
AU - Araoud A.
AU - Ghorbel E.
AU - Ghorbel F.
PY - 2025
SP - 805
EP - 812
DO - 10.5220/0013183500003890
PB - SciTePress