In this paper, an approach to unsupervised pattern classifiation is discussed. The classification scheme is based on an approximation of the probability densities of each class under the assumption that the input patterns are of a normal mixture. The proposed technique for identifying the mixture does not require prior information. The description of the mixture in terms of convexity allows to determine, from a totally unlabeled set of samples, the number of components and, for each of them, approximate values of the mean vector, the covariance matrix, and the a priori probability. Discriminant functions can then be constructed. Computer simulations show that the procedure yields decision rules whose performances remain close to the optimum Bayes minimum error-rate, while involving only a small amount of computation.