Residual bilinearization combined with kernel-unfolded partial least-squares: A new technique for processing non-linear second-order data achieving the second-order advantage

Abstract

A new second-order multivariate calibration model is presented which allows one to process matrix data showing a non-linear relationship between signal and concentration, and achieving the important second-order advantage. The latter property permits analyte quantitation even in the presence of unexpected sample components, i.e., those not present in the calibration set. The model is based on a combination of residual bilinearization, which provides the second-order advantage, and kernel partial least-squares of unfolded data, a flexible non-linear version of partial least-squares. The latter one involves projection of the measured data onto a non-linear space, which in the present case consists of a set of Gaussian radial basis functions. Simulations concerning two ideal systems are analyzed: one where the signal-concentration relation is quadratic with positive deviations from linearity, and another one where it is sigmoidal. The results are favorably compared with those provided by several artificial neural network approaches. Two experimental systems are also studied, involving the analysis of: 1) the lipid degradation product malondialdehyde in olive oil samples, where the background oil provides a strong interferent signal, and 2) the antibiotic amoxicillin in the presence of the anti-inflammatory salicylate as interferent. The results for these experimental cases are also encouraging.