Nonlinear partial least squares modelling II. Spline inner relation

Abstract

Wold, S., 1992. Nonlinear partial least squares modelling. II. Spline inner relation. Chemometrics and Intelligent Laboratory Systems, 14: 71–84. A common problem in chemometrics is to relate one data matrix, X, to another, Y. Typical applications are found in multivariate calibration ( X = signals, Y = concentrations), structure ( X)-property ( Y), and composition ( X)-property ( Y) relationships, and process optimization ( X = process variables, Y = process output). For this problem, PLS modelling has been found valuable (PLS = partial least squares projections to latent structures). The ordinary PLS model is linear in its relation between X and Y, however, and hence often works well only over limited intervals of X. It is therefore of some interest to develop nonlinear PLS models to increase the range of PLS modelling. A PLS model with a nonlinear inner relation is presented in a general form with a spline function for inner relation. The estimation algorithm is consistent with Höskuldsson's PLS principles. The ‘spline-PLS’ model (SPL-PLS) is illustrated with an application to quantitative structure—activity relationships. The relationships between SPL-PLS and neural networks are discusssed.