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1 INRIA Rocquencourt

Abstract : Gaussian clustering models are useful both for understanding and suggesting powerful criteria. Banfield and Raftery 1993 have considered a parametrization of the variance matrix Ek of a cluster Pk in terms of its eigenvalue decomposition, Ek = lkDkAkD-k, lk where lk defines the volume of Pk, Dk is an orthogonal matrix which defines its orientation and Ak is a diagonal matrix with determinant 1 which defines its shape. This parametrization allows us to propose many general clustering criteria from the simplest one spherical cluster with equal volumes which leads to the classical k-means criterion to the most complex one unknown and different volumes, orientations and shapes for all clusters. Methods of optimization to derive the maximum likelihood estimates as well as the practical usefulness of these models are discussed. We especially analyze the influence of the volumes of clusters. We report Monte-Carlo simulations and an application on stellar data which dramatically illustrated the relevance of allowing clusters to have different volumes.

Autor: Gilles Celeux - Gérard Govaert



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