Geodesically-convex optimization for averaging partially observed covariance matrices - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2020

Geodesically-convex optimization for averaging partially observed covariance matrices

Résumé

Symmetric positive definite (SPD) matrices permeates numerous scientific disciplines, including machine learning, optimization, and signal processing. Equipped with a Rieman-nian geometry, the space of SPD matrices benefits from compelling properties and its derived Riemannian mean is now the gold standard in some applications, e.g. brain-computer interfaces (BCI). This paper addresses the problem of averaging covariance matrices with missing variables. This situation often occurs with inexpensive or unreliable sensors, or when artifact-suppression techniques remove corrupted sensors leading to rank deficient matrices, hindering the use of the Riemannian geometry in covariance-based approaches. An alternate but questionable method consists in removing the matrices with missing variables , thus reducing the training set size. We address those limitations and propose a new formulation grounded in geodesic convexity. Our approach is evaluated on generated datasets with a controlled number of missing variables and a known baseline, demonstrating the robustness of the proposed estimator. The practical interest of this approach is assessed on real BCI datasets. Our results show that the proposed average is more robust and better suited for classification than classical data imputation methods.
Fichier principal
Vignette du fichier
yger20a.pdf (664.63 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02984423 , version 1 (30-10-2020)

Identifiants

  • HAL Id : hal-02984423 , version 1

Citer

Florian Yger, Sylvain Chevallier, Quentin Barthélemy, Suvrit Sra. Geodesically-convex optimization for averaging partially observed covariance matrices. Asian Conference on Machine Learning (ACML), Nov 2020, Bangkok, Thailand. pp.417 - 432. ⟨hal-02984423⟩
127 Consultations
125 Téléchargements

Partager

Gmail Facebook X LinkedIn More