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

Authors:
Robert Sabatier;Christelle Reynès
Affiliations:
Laboratoire de Physique Industrielle et Traitement de l'Information, EA 2415, Facult de Pharmacie, 15 avenue Charles Flahault, BP 14491, 34093 Montpellier Cedex 5, France;Laboratoire de Physique Industrielle et Traitement de l'Information, EA 2415, Facult de Pharmacie, 15 avenue Charles Flahault, BP 14491, 34093 Montpellier Cedex 5, France
Venue:
Computational Statistics & Data Analysis
Year:
2008

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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^(C) 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).