Discriminant analysis based on mixture distribution models and classification

Mixture distribution models can be used for modeling of non-homogeneous or heterogeneous structure of a population with the interested characteristics. Mixture distribution models can be also used for model based discrimination and classification. Discrimination based on the mixture distribution models is called mixture discriminant analysis. Each observation in the test data is classified with the mixture distribution models of the training data by using Bayes classification rule. This classification method based on similarity between an observation and a mixture distribution model in mixture discriminant analysis. In this PhD Thesis, we fit the mixture of multivariate normal distribution models for the training data. The test data is classified by using average Bhattacharyya distance. Therefore, for the multivariate data we emlpoy the mixture discriminant analysis based on similarity between two mixture distribution models as an alternative the Bayes classification rule. In addition, we use mixture discriminant analysis with neural networks. The parameters of the mixture of multivariate normal distributions were estimated with neural networks.