A non-linear nested partial least-squares algorithm

A nested partial least-squares (PLS) algorithm is proposed for the modelling of non-linear systems in the presence of multicollinearity. The nested algorithm comprises both an inner and outer PLS algorithm. The objective of the outer algorithm is to extract those latent variables that will form the basis of the final application whilst the role of the inner algorithm is to derive the weight vectors for the outer PLS algorithm. Wold's non-linear PLS algorithm and the error-based weight updating procedure are special cases. The nested PLS algorithm is illustrated by application to simulated data and an industrial NIR spectral data set.