Non-linear principal components analysis using genetic programming

Principal components analysis (PCA) is a standard statistical technique, which is frequently employed in the analysis of large highly correlated data-sets. As it stands, PCA is a linear technique which can limit its relevance to the highly nonlinear systems frequently encountered in the chemical process industries. Several attempts to extend linear PCA to cover nonlinear data sets have been made, and will be briefly reviewed in this paper. We propose a symbolically oriented technique for nonlinear PCA, which is based on the genetic programming (GP) paradigm. Its applicability will be demonstrated using two simple nonlinear systems and industrial data collected from a distillation column. It is suggested that the use of the GP-based nonlinear PCA algorithm achieves the objectives of nonlinear PCA, while giving high a degree of structural parsimony