A probabilistic view on Riemannian machine learning models for SPD matrices

• URL: http://arxiv.org/abs/2505.02402v1
• Date: Mon, 05 May 2025 06:50:06 GMT
• Title: A probabilistic view on Riemannian machine learning models for SPD matrices
• Authors: Thibault de Surrel, Florian Yger, Fabien Lotte, Sylvain Chevallier,
• Abstract summary: We show how different machine learning tools on the $mathcalP_d$ of Symmetric Positive Definite (SPD) matrices can be united under a probabilistic framework.<n>By showing that those distributions are pervasive in the tools used on $mathcalP_d$, we allow for other machine learning tools to be extended to $mathcalP_d$.
• Score: 6.7523635840772505
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The goal of this paper is to show how different machine learning tools on the Riemannian manifold $\mathcal{P}_d$ of Symmetric Positive Definite (SPD) matrices can be united under a probabilistic framework. For this, we will need several Gaussian distributions defined on $\mathcal{P}_d$. We will show how popular classifiers on $\mathcal{P}_d$ can be reinterpreted as Bayes Classifiers using these Gaussian distributions. These distributions will also be used for outlier detection and dimension reduction. By showing that those distributions are pervasive in the tools used on $\mathcal{P}_d$, we allow for other machine learning tools to be extended to $\mathcal{P}_d$.

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