Random matrix theory improved Fréchet mean of symmetric positive definite matrices
Florent Bouchard, Ammar Mian, Malik Tiomoko, Guillaume Ginolhac, Frederic Pascal
Abstract
In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fréchet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory based method that estimates Fréchet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.
BibTeX
@inproceedings{
bouchard2024random,
title={Random matrix theory improved Fr\'echet mean of symmetric positive definite matrices},
author={Florent Bouchard and Ammar Mian and Malik Tiomoko and Guillaume Ginolhac and Frederic Pascal},
booktitle={Forty-first International Conference on Machine Learning},
year={2024},
url={https://openreview.net/forum?id=uQiFsBil3p}
}