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

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  • Sabatier, Robert
  • Reynès, Christelle

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).

Suggested Citation

  • Sabatier, Robert & Reynès, Christelle, 2008. "Extensions of simple component analysis and simple linear discriminant analysis using genetic algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4779-4789, June.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4779-4789
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    1. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    2. S. K. Vines, 2000. "Simple principal components," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(4), pages 441-451.
    3. J. N. R. Jeffers, 1967. "Two Case Studies in the Application of Principal Component Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 16(3), pages 225-236, November.
    4. Valentin Rousson & Theo Gasser, 2004. "Simple component analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(4), pages 539-555, November.
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