Generalized dirichlet mixture matching projection for supervised linear dimensionality reduction of proportional data

Abstract

In this paper, a novel effective method to reduce the dimensionality of labeled proportional data is introduced. Most well-known existing linear dimensionality reduction methods rely on solving the generalized eigen value problem which fails in certain cases such as sparse data. The proposed algorithm is a linear method and uses a novel approach to the problem of dimensionality reduction to solve this problem while resulting higher classification rates. Data is assumed to be from two different classes where each class is matched to a mixture of generalized Dirichlet distributions after projection. Jeffrey divergence is then used as a dissimilarity measure between the projected classes to increase the inter-class variance. To find the optimal projection that yields the largest mutual information, genetic algorithm is used. The method is especially designed as a preprocessing step for binary classification, however, it can handle multi-modal data effectively due to the use of mixture models and therefore can be used for multi-class problems as well.