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Communication Dans Un Congrès Année : 2020

Riemannian framework for robust covariance matrix estimation in spiked models

Résumé

This paper aims at providing an original Riemannian geometry to derive robust covariance matrix estimators in spiked models (i.e. when the covariance matrix has a low-rank plus identity structure). The considered geometry is the one induced by the product of the Stiefel manifold and the manifold of Hermitian positive definite matrices, quotiented by the uni-tary group. One of the main contributions is to consider a Riemannian metric related to the Fisher information metric of elliptical distributions, leading to new representations for the tangent spaces and a new retraction. A new robust covari-ance matrix estimator is then obtained as the minimizer of Tyler's cost function, redefined directly on the set of low-rank plus identity matrices, and computed with the aforementioned tools. The main interest of this approach is that it appears well suited to the cases where the sample size is lower than the dimension , as illustrated by numerical experiments.
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Dates et versions

hal-02571084 , version 1 (12-05-2020)

Identifiants

Citer

Florent Bouchard, Arnaud Breloy, Guillaume Ginolhac, Frédéric Pascal. Riemannian framework for robust covariance matrix estimation in spiked models. ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2020, Barcelona, Spain. ⟨10.1109/icassp40776.2020.9054726⟩. ⟨hal-02571084⟩
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