# Random matrix theory improved Fr'echet mean of symmetric positive definite matrices

arXiv: https://arxiv.org/abs/2405.06558 · HTML: https://mlsanity.com/paper/2405.06558/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 10 May 2024.

## Builds on (most cited first, 11 of 11)

- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [BreizhCrops: A Time Series Dataset for Crop Type Mapping](https://mlsanity.com/paper/1905.11893/) (2019)
- [On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry](https://mlsanity.com/paper/2106.00286/) (2021)
- [Geometric Mean Metric Learning](https://mlsanity.com/paper/1607.05002/) (2016)
- [Differential Privacy Over Riemannian Manifolds](https://mlsanity.com/paper/2111.02516/) (2021)
- [Regularized M-estimators of scatter matrix](https://mlsanity.com/paper/1405.2528/) (2014)
- [Differentially Private Fr'echet Mean on the Manifold of Symmetric Positive Definite (SPD) Matrices with log-Euclidean Metric](https://mlsanity.com/paper/2208.04245/) (2022)
- [Random Matrix Improved Covariance Estimation for a Large Class of Metrics](https://mlsanity.com/paper/1902.02554/) (2019)
- [Random matrix-improved estimation of covariance matrix distances](https://mlsanity.com/paper/1810.04534/) (2018)

## Built on by (most cited first, 1 of 1)

- [Elliptical Wishart distributions: information geometry, maximum likelihood estimator, performance analysis and statistical learning](https://mlsanity.com/paper/2411.02726/) (2024)

## Abstract (arXiv)

In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr'echet 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 Fr'echet 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.