Genetic algorithms applied to the selection of factors in principal component regression

Using principal component regression (PCR) as a multivariate calibration tool, always brings up the question what subset of factors, i.e. principal components (PCs) gives the best calibration model. Normally factor selection is based on deterministic methods like top–down procedures, forward–backward-stepwise variable selection or correlated principal component regression (CPCR). In contrast to this, we applied a stochastic method, i.e. a genetic algorithm (GA) for factor selection in this paper. A new kind of fitness function was applied which combined the prediction error of the calibration and an independent validation set. The performance of eigenvalue and correlation ranking was compared. A general statistical criterion for judging the significance of differences between individual calibration models is introduced. In this context it could be shown that for the uncertainties of the standard deviations representing the prediction errors a very simple approximation formula holds which only includes the number of standards. For the current applications it is shown that the GA gives a result very close to CPCR-solutions.