Extensions of simple component analysis and simple linear discriminant analysis using genetic algorithms

Abstract

Extensions of Simple Component Analysis are proposed. Two methods are obtained: a new Simple Component Analysis and a Simple Linear Discriminant Analysis. These two methodologies use Genetic Algorithms, optimize a criterion (derived from the usual method) and add constraints. The objective is to obtain loadings constituted of a small number of integers determining blocks of variables. The programs implementing the methods have been developed using the R© language. Four applications are made and show a good robustness of the algorithms and a proximity to the optimal solution (from the usual PCA and LDA).