A fast and efficient Modal EM algorithm for Gaussian mixtures

In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either nonparametrically or using finite mixture models. Thus, clusters are closely related to certain regions around the density modes, and every cluster corresponds to a bump of the density. The Modal Expectation-Maximization (MEM) algorithm is an iterative procedure that can identify the local maxima of any density function. In this contribution, we propose a fast and efficient MEM algorithm to be used when the density function is estimated through a finite mixture of Gaussian distributions with parsimonious component-covariance structures. After describing the procedure, we apply the proposed MEM algorithm on both simulated and real data examples, showing its high flexibility in several contexts.