A Clustering Bayesian Approach for Multivariate Non-Ordered Circular Data

Christophe Abraham (1) , Rémi Servien (2) , Nicolas Molinari (3)

1 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 ToxAlim - ToxAlim
3 IMAG - Institut Montpelliérain Alexander Grothendieck

This paper presents a Bayesian framework for the clustering of multivariate directional or circular data. We introduce a hierarchical model that combines Projected Normal distributions and a Dirichlet Process. The parameters of the model are then inferred using a Metropolis-Hastings within Gibbs algorithm. Simulated datasets are analyzed to study the influence of the parameters of the model. Then, the benefits of our approach are illustrated by clustering real data from the positions of five separate radiotherapy x-ray beams on a circle.

Mots clés: Circular data; Dirichlet process; Non-ordered multivariate data; Projected Normal Distribution; Radiotherapy machine data; Unsupervised clustering

Domaines: Statistiques [math.ST]

Christophe Abraham, Rémi Servien, Nicolas Molinari. A Clustering Bayesian Approach for Multivariate Non-Ordered Circular Data. 2017. ⟨hal-01326166v4⟩