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Biostatistics Advance Access published online on April 27, 2007
Biostatistics, doi:10.1093/biostatistics/kxm012
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Model-based clustering on the unit sphere with an illustration using gene expression profiles

Jean-Luc Dortet-Bernadet*

Institut de Recherche Mathématique Avancée (IRMA), UMR 7501 CNRS, Université Louis Pasteur, Strasbourg, France dortet{at}math.u-strasbg.fr

Nicolas Wicker

Laboratoire de Bioinformatique et Génomique Intégratives, Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), UMR 7104, Université Louis Pasteur, Strasbourg, France wicker{at}igbmc.u-strasbg.fr

* To whom correspondence should be addressed.

We consider model-based clustering of data that lie on a unit sphere. Such data arise in the analysis of microarray experiments when the gene expressions are standardized so that they have mean 0 and variance 1 across the arrays. We propose to model the clusters on the sphere with inverse stereographic projections of multivariate normal distributions. The corresponding model-based clustering algorithm is described. This algorithm is applied first to simulated data sets to assess the performance of several criteria for determining the number of clusters and to compare its performance with existing methods and second to a real reference data set of standardized gene expression profiles.

Keywords: Clustering; Directional data; Microarrays; Mixture

Received November 22, 2005; revised September 14, 2006; revised November 24, 2006; revised January 19, 2007; accepted for publication March 9, 2007.


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