Misturas finitas de densidades beta e de Dirichlet aplicadas em análise discriminante

Abstract

In many Discriminant Analysis (DA) applications the observations of the variables in the characteristic vector are confined on the interval (0,1), p.e, pixel classification in digital images. In this work, we investigated the use of the Bayes Classifier (BC) for these applications, modeling the distributions in the classes using Finite Mixture Density Betas and the Dirichlet. To investigate and evaluate this model, we developed a simulation study, analyzing the estimation of densities and the parameters, as well as the Classification Error Rates (ER). Problems were simulated with different structures, relative to the number of components, training set size, overlap and class distribution. The results of the study suggest that the models evaluated are able to adjust to the different problems considered, from the simplest to the most complex, in terms of modeling observations for classification purposes. With real data, situations where the class distributions are unknow, the BC’s with the implemented models presented reasonable TE when compared to other more usual classifiers. As a limitation, the modeling presents better performances with a relatively high number of observations in the training set.