Random matrix theory improved Fréchet mean of symmetric positive definite matrices - Laboratoire d’Informatique, Systèmes, Traitement de l’Information et de la Connaissance
Communication Dans Un Congrès Année : 2024

Random matrix theory improved Fréchet mean of symmetric positive definite matrices

Résumé

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 stateof-the-art methods.
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Dates et versions

hal-04694884 , version 1 (11-09-2024)

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Florent Bouchard, Ammar Mian, Malik Tiomoko, Guillaume Ginolhac, Frédéric Pascal. Random matrix theory improved Fréchet mean of symmetric positive definite matrices. International Conference on Machine Learning (ICML), Jul 2024, Vienna, Austria. ⟨hal-04694884⟩
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