Bayes classifier based on tree-structured Gaussian mixtures

Abstract

A novel approach is proposed to constructing a Bayes classifier in a multidimensional space of features by using tree-structured Gaussian mixtures as estimates of class-conditional probability density functions. A training procedure is developed for the classifier that is reduced to finding numbers of mixture components and their thresholds in order to realize rejections for the given classes. The mixture parameters are optimized by a cross-validation method. Classification error rate is estimated on a set of 3D vectors of textual features of a monochrome image. Comparative error rates are obtained for classifiers that use histograms, individual Gaussian densities, and Gaussian mixtures constructed using the EM (expectation-maximization) algorithm. The practical application of the developed classifier is illustrated by results of image segmentation for a satellite picture. The image represents a fragment of the Earth surface and it is obtained using the Google Earth program.