Riemannian Optimization for Non-Centered Mixture of Scaled Gaussian Distributions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IEEE Transactions on Signal Processing Année : 2023

Riemannian Optimization for Non-Centered Mixture of Scaled Gaussian Distributions

Résumé

This paper studies the statistical model of the noncentered mixture of scaled Gaussian distributions (NC-MSG). Using the Fisher-Rao information geometry associated with this distribution, we derive a Riemannian gradient descent algorithm. This algorithm is leveraged for two minimization problems. The first is the minimization of a regularized negative loglikelihood (NLL). The latter makes the trade-off between a white Gaussian distribution and the NC-MSG. Conditions on the regularization are given so that the existence of a minimum to this problem is guaranteed without assumptions on the samples. Then, the Kullback-Leibler (KL) divergence between two NC-MSG is derived. This divergence enables us to define a second minimization problem. The latter is the computation of centers of mass of several NC-MSGs. Numerical experiments show the good performance and the speed of the Riemannian gradient descent on the two problems. Finally, a Nearest centroïd classifier is implemented leveraging the KL divergence and its associated center of mass. Applied on the large-scale dataset Breizhcrops, this classifier shows good accuracies and robustness to rigid transformations of the test set.
Fichier principal
Vignette du fichier
DEMR23059.pdf (1.73 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : Copyright (Tous droits réservés)

Dates et versions

hal-04171793 , version 1 (26-07-2023)

Identifiants

Citer

Antoine Collas, Arnaud Breloy, Chengfang Ren, Guillaume Ginolhac, Jean-Philippe Ovarlez. Riemannian Optimization for Non-Centered Mixture of Scaled Gaussian Distributions. IEEE Transactions on Signal Processing, 2023, 71, pp.2475-2490. ⟨10.1109/TSP.2023.3290354⟩. ⟨hal-04171793⟩
17 Consultations
2 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More