Fuzzy clustering for the estimation of the parameters of the components of mixtures of normal distributions

A method is described, based on clustering, for estimating the parameters of a finite mixture of normal distributions. Cluster centers are computed by fuzzy clustering, these centers being initial conditions for fuzzy partition based on maximum-likelihood estimation. The algorithm incorporates unsupervised tracking of initial cluster centers during its first stage. The number of underlying components in the mixture is derived from performance measures, based on fuzzy hypervolume and density criteria. The algorithm has been tested on several simulated data sets (mixtures of univariate distributions and of bivariate distributions), and on a real data set.