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

Amal Araoud, Enjie Ghorbel, Faouzi Ghorbel

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 li

External IDs:dblp:conf/icaart/AraoudGG25