A clustering Bayesian approach for multivariate non-ordered circular data. (December 2019)

• Record Type: Journal Article
• Authors: Abraham, Christophe; Servien, Rémi; Molinari, Nicolas
• Is Part Of: Statistical modelling. Volume 19:Number 6(2019)
• Page Start: 595
• Page End: 616
• Publication Date: 2019-12
• Subjects: circular data -- dirichlet process -- non-ordered multivariate data -- projected normal distribution -- radiotherapy machine data -- unsupervised clustering; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X18790420
• Languages: English
• ISSNs: 1471-082X

Abstract

This article presents a Bayesian model for the clustering of non-ordered multivariate directional or circular data. The particular trait of our data is that each single observation is made up ofk ≥ 2 non-ordered points on the circle. We introduce a hierarchical model that combines a symmetrization technique, projected normal distributions and a Dirichlet process. One parameter is introduced to model the non-ordered trait and another one to control the variability of the angles on the circle. An informative prior on the relative locations of thek angles is also provided. The gain of the symmetrization is highlighted by a theoretical study. The parameters of the model are then inferred using a Metropolis–Hastings-within-Gibbs algorithm. Simulated datasets are analysed to study the sensitivity to hyperparameters. Then, the benefits of our approach are illustrated by clustering real data made up of the positions of five separate radiotherapy X-ray beams on a circle.