A Combined Stochastic and Deterministic Approach for Classification Using Generalized Mixture Densities

This work investigates a combined stochastic and deterministic optimization approach for multivariate mixture density estimation. Mixture probability density models are selected and optimized by combining the optimization characteristics of a multiagent stochastic optimization algorithm based on evolutionary programming and the expectation-maximization algorithm. Unlike the traditional finite mixture model, generally composed of a sum of normal component densities, the generalized mixture model is composed of shape-adaptive components. Rissanen's minimum description length criterion provides the selection mechanism for evaluating mixture model fitness. The classification problem is approached by optimizing a mixture density estimate for each class. A comparison of each class's posterior probability (Bayes rule) provides the classification decision procedure. A classification problem is posed, and the classification performance of the derived generalized mixture models is compared with the performance of mixture models generated using normally distributed components. While both approaches produced excellent classification results, the generalized mixture approach produced more parsimonious density models from the training data.