A probabilistic view on Riemannian machine learning models for SPD matrices
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917056092307456 |
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| author | de Surrel, Thibault Yger, Florian Lotte, Fabien Chevallier, Sylvain |
| author_facet | de Surrel, Thibault Yger, Florian Lotte, Fabien Chevallier, Sylvain |
| contents | 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 $\mathcal{P}_d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A probabilistic view on Riemannian machine learning models for SPD matrices de Surrel, Thibault Yger, Florian Lotte, Fabien Chevallier, Sylvain Machine Learning Statistics Theory 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 $\mathcal{P}_d$. |
| title | A probabilistic view on Riemannian machine learning models for SPD matrices |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2505.02402 |