Estimation du centre et du rayon d’une hypersphère à l’aide d’une loi a priori de Von Mises-Fisher et d’un algorithme EM

Résumé

This article introduces an extension of an EM algorithm (Expectation Maximization) published recently by the authors allowing to estimate jointly the center and the radius of an hypersphere as well as the statistical model hyperparameters acounting that the observations are located on a part of the hypersphere. The proposed method relies on the introduction of latent variables having a von Mises Fisher prior. This statistical model allows to express the complete data likelihood, which expectancy conditionned to the observed data has a known distribution resulting in a simple and efficient EM algorithm. The performances of this estimation algorithm are assessed through simulations performed in a bidimensinal case with promising results.