The paper "Gaussian Parsimonious Clustering Models" by Gilles Celeux and Gérard Govaert discusses the use of Gaussian mixture models for clustering analysis. The authors propose a parametrization of the variance matrices of mixture components, allowing for flexible and powerful clustering criteria. This parametrization, based on the eigenvalue decomposition of the variance matrices, enables the specification of different assumptions about cluster volumes, orientations, and shapes. The paper derives maximum likelihood estimates for these models and discusses the practical usefulness of these models, particularly focusing on the influence of cluster volumes. Monte-Carlo simulations and an application to stellar data are presented to illustrate the effectiveness of the proposed models, highlighting the importance of allowing clusters to have different volumes. The paper concludes by recommending the use of models that allow for different volumes in Gaussian mixture models, as they can better capture various clustering structures and are more robust in practical applications.The paper "Gaussian Parsimonious Clustering Models" by Gilles Celeux and Gérard Govaert discusses the use of Gaussian mixture models for clustering analysis. The authors propose a parametrization of the variance matrices of mixture components, allowing for flexible and powerful clustering criteria. This parametrization, based on the eigenvalue decomposition of the variance matrices, enables the specification of different assumptions about cluster volumes, orientations, and shapes. The paper derives maximum likelihood estimates for these models and discusses the practical usefulness of these models, particularly focusing on the influence of cluster volumes. Monte-Carlo simulations and an application to stellar data are presented to illustrate the effectiveness of the proposed models, highlighting the importance of allowing clusters to have different volumes. The paper concludes by recommending the use of models that allow for different volumes in Gaussian mixture models, as they can better capture various clustering structures and are more robust in practical applications.