Unsupervised clustering of multivariate circular data

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

1 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 Unité Médicale des Maladies Auto-Inflammatoires (Centre de Référence)

An unsupervised clustering problem is studied in this paper. The originality of this problem lies in the data, which consist of the positions of five separate x-ray beams on a circle. The five x-ray beam "projectors" are positioned around each patient on a predefined circle. However, similarities exist in positioning for certain groups of patients, and we aim to describe these similarities with the goal of creating pre-adjustment settings that could help save time during x-ray positioning. We therefore performed unsupervised clustering of observed x-ray positions. Because the data for each patient consists of five angle measurements, Euclidean distances are not appropriated. Furthermore, $k$-means algorithm, usually used for minimising corresponding distortion can not be computed because centers of clusters are not calculables. We present here solutions to these problems. First, we define a suitable distance on the circle. Then, we adapt an algorithm based on simulated annealing to minimize distortion. This algorithm is shown to be theoretically convergent. Finally, simulations on simulated and real data are presented.

Mots clés: Circular data; Radiotherapy machine data.; Radiotherapy machine data; Unsupervised clustering

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christophe Abraham, Nicolas Molinari, Rémi Servien. Unsupervised clustering of multivariate circular data. Statistics in Medicine, 2013, 32 (8), pp.1376-1382. ⟨10.1002/sim.5589⟩. ⟨hal-00674196v4⟩