GENERALIZED PRINCIPAL COMPONENT ANALYSIS WITH RESPECT TO INSTRUMENTAL VARIABLES VIA UNIVARIATE SPLINE TRANSFORMATIONS

A method is proposed for a nonlinear structural analysis of multivariate data. that is termed a generalized principal component analysis with respect to instrumental variables via spline transformations (or spline-PCAIV). This method combines features of multiresponse additive spline regression analysis and principal component analysis. The solution of the corresponding linear problem belongs to the set of the feasible solutions and constitutes the first step of the associated iterative algorithm. Introducing adapted metrics in principal component analysis leads to an interpretation of the method as an optimal canonical analysis. Examples related to distorted pattern recognition, multivariate regression analysis and nonlinear discriminant analysis show how spline-PCAIV works.