Canonical Correlation after spline transformation for Dimension Reduction

Keywords: canonical analysis, dimension reduction, spline

Abstract: To effectively study a large number of variables is no easy task. We consider reducing the dimension of the input variables. Our dimension reduction method is similar to slice inverse regression but easier to implement with a direct reference to canonical correlation. In a model h(Y)~ X, we project h onto a linear space of B-spline functions. Then the direction of X and the parameters of B-spline functions are computed simultaneously by canonical correlation analysis. A chi-square test is used to determine the number of directions needed from X. Examples are used to demonstrate the usefulness of this approach.