ANÁLISIS DE CORRELACIÓN CANÓNICA USANDO ALGORITMOS GENÉTICOS

Abstract

Canonical Correlation Analysis (CCA) is an exploratory method of Multivariate Analysis, it studies the relationship between two sets of quantitative variables observed in the same set of individuals. It obtains new variables that are linear combination of the original variables of the two groups, such that the correlation between the projections of the data of this new variables is maximum. There are several proposals to determine canonical correlations and canonical vectors using techniques of numerical linear algebra, that is, in the
formulation of Lagrange, CCA becomes a generalized eigenvalues and eigenvectors problem, assuming that the variance-covariance matrices are invertible. On the other hand, Genetic Algorithms (GA) are adaptive methods used to solve global optimization problems. When the invertibility condition is not satisfied by the variance-covariance matrices, we propose in this paper, use GA to solve the problem of CCA directly from the definition. We test the proposal with problems reported in the literature and also presents a real application
of CCA to data of soil carbon in the area of Teziutlan, Puebla.