External Single-Set Components Analysis Of Multiple Criterion/Multiple Predictor Variables

Although much progress has been made in clarifying the properties of canonical correlation analysis in order to enhance its applicability, there are several remaining problems. Canonical variates do not always represent the observed variables even though the canonical correlation is high. In addition, canonical solutions are often difficult to interpret. This paper presents a method designed to deal with these two problems. Instead of maximizing the correlation between unobserved variates, the sum of squared inter-set loadings is maximized. Contrary to the canonical correlation solution, this method ensures that the shared variance between predictor variates and criterion variables is maximal. Instead of extracting variates from both criterion and predictor variables, only one set of components (from the predictor variables) is constructed. Without loss of common variance, an orthogonal rotation is applied to the resulting loadings in order to simplify structure.