Mixture densities constitute a rich family of models that can be used in several data mining and machine learning applications, for instance, clustering. Although practical algorithms exist for learning such models from data, these algorithms typically do not scale very well with large datasets. Our approach, which builds on previous work by other authors, offers an acceleration of the EM algorithm for Gaussian mixtures by precomputing and storing sufficient statistics of the data in the nodes of a kd-tree. Contrary to other works, we obtain algorithms that strictly increase a lower bound on the data log-likelihood in every learning step. Experimental results illustrate the validity of our approach.