Random matrix theory improved Fréchet mean of symmetric positive definite matrices
This work addresses a bottleneck in machine learning tasks involving covariance matrices, such as EEG and hyperspectral data analysis, by improving mean estimation efficiency.
The paper tackles the problem of computing Fréchet means on symmetric positive definite matrices, which is challenging with low sample support and many matrices, by introducing a random matrix theory-based method that significantly outperforms state-of-the-art methods on synthetic, EEG, and hyperspectral datasets.
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.