Biplots in Canonical Correlation Analysis

• Autores: Jan Graffelman
• Localización: XXX Congreso Nacional de Estadística e Investigación Operativa y de las IV Jornadas de Estadística Pública: actas, 2007, ISBN 978-84-690-7249-3
• Idioma: inglés
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• Resumen

  • Canonical correlation analysis (CCO) is a classical multivariate method devel- oped in the thirties by Hotelling. Originally, the output of a canonical correlation analysis was highly numerical, and the interpretation was based on canonical correlations, weights and loadings. The introduction of a biplot for CCO has been of great practical value for the interpretation of the results. CCO allows for a biplot of the between-set correlation matrix Rxy from which the relationships between the two sets of variables can be inferred. Whereas the classical biplots from a principal component analysis represent both cases and variables, a biplot obtained by CCO only represents the variables of the X and Y set. The cases (samples) are completely absent in the CCO biplot. We will seek for ways to represent the cases of the original data matrices in the CCO biplot by general- ized least squares and address the issue of goodness of ¯t of the representations obtained.