The mixture model is undoubtedly one of the greatest contributions to clustering. For continuous data, Gaussian models are often used and the Expectation-Maximization (EM) algorithm is particularly suitable for estimating parameters from which clustering is inferred. If these models are particularly popular in various domains including image clustering, they however suffer from the dimensionality and also from the slowness of convergence of the EM algorithm. However, the Classification EM (CEM) algorithm, a classifying version, offers a fast convergence solution while dimensionality reduction still remains a challenge. Thus we propose in this paper an algorithm combining simultaneously and non-sequentially the two tasks --Data embedding and Clustering-- relying on Principal Component Analysis (PCA) and CEM. We demonstrate the interest of such approach in terms of clustering and data embedding. We also establish different connections with other clustering approaches.

翻译：混合模型无疑是聚类领域最重要的贡献之一。对于连续数据，通常采用高斯模型，而期望最大化（EM）算法特别适用于估计参数并由此推断聚类。尽管这些模型在图像聚类等多个领域广受欢迎，但它们仍面临维度灾难以及EM算法收敛速度缓慢的问题。然而，分类EM（CEM）算法作为一种分类版本，提供了快速收敛的解决方案，但降维仍是一个挑战。因此，本文提出一种算法，基于主成分分析（PCA）和CEM，同时且非顺序地结合数据嵌入与聚类两项任务。我们证明了该方法在聚类和数据嵌入方面的优势，并建立了与其他聚类方法的不同联系。