Deflation based nonlinear canonical correlation analysis

Abstract

This paper introduces two new techniques for determining nonlinear canonical correlation coefficients between two variable sets. A genetic strategy is incorporated to determine these coefficients. Compared to existing methods for nonlinear canonical correlation analysis (NLCCA), the benefits here are that the nonlinear mapping requires fewer parameters to be determined, consequently a more parsimonious NLCCA model can be established which is therefore simpler to interpret. A further contribution of the paper is the investigation of a variety of nonlinear deflation procedures for determining the subsequent nonlinear canonical coefficients. The benefits of the new approaches presented are demonstrated by application to an example from the literature and to recorded data from an industrial melter process. These studies show the advantages of the new NLCCA techniques presented and suggest that a nonlinear deflation procedure should be considered.