Gaussian parsimonious clustering models, introduced by Gilles Celeux and Gérard Govaert, provide a flexible framework for clustering data by parametrizing the variance matrices of Gaussian mixture components. The variance matrix of each cluster is decomposed into eigenvalues and eigenvectors, allowing for different cluster volumes, orientations, and shapes. This approach generalizes traditional clustering methods, such as k-means, by allowing clusters to have varying volumes, orientations, and shapes. The models are estimated using the EM algorithm, and the paper discusses various clustering scenarios, including spherical, diagonal, and general models. The authors analyze the impact of cluster volumes on clustering performance and demonstrate the effectiveness of these models through Monte-Carlo simulations and an application on stellar data. The paper also compares different models and highlights the importance of allowing different cluster volumes for more accurate clustering. The results show that models with different cluster volumes outperform those with equal volumes in many cases, especially when clusters have different sizes and shapes. The paper concludes that allowing different cluster volumes is a valuable approach in clustering analysis.Gaussian parsimonious clustering models, introduced by Gilles Celeux and Gérard Govaert, provide a flexible framework for clustering data by parametrizing the variance matrices of Gaussian mixture components. The variance matrix of each cluster is decomposed into eigenvalues and eigenvectors, allowing for different cluster volumes, orientations, and shapes. This approach generalizes traditional clustering methods, such as k-means, by allowing clusters to have varying volumes, orientations, and shapes. The models are estimated using the EM algorithm, and the paper discusses various clustering scenarios, including spherical, diagonal, and general models. The authors analyze the impact of cluster volumes on clustering performance and demonstrate the effectiveness of these models through Monte-Carlo simulations and an application on stellar data. The paper also compares different models and highlights the importance of allowing different cluster volumes for more accurate clustering. The results show that models with different cluster volumes outperform those with equal volumes in many cases, especially when clusters have different sizes and shapes. The paper concludes that allowing different cluster volumes is a valuable approach in clustering analysis.