Spectral pre-processing and non-linear calibration with convolutional kernel partial least-squares. Teaching new tricks to an old dog

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A recent trend in multivariate calibration of non-linear systems is to simplify data processing models, avoiding, if possible, some complex deep learning approaches. Contributing to this line of work, convolutional kernel partial least-squares (CKPLS) is introduced both for finding the best spectral pre-processing procedure for reducing the impact of radiation scattering and for handling non-linearities in the data. CKPLS is a combination of a previous convolutional step for pre-processing the spectra with the well-known kernel PLS regression model for coping with non-linear relationships between spectral signatures and analyte concentrations or target sample properties. The convolutional step is driven by particle swarm optimization (PSO), which estimates the coefficients of a moving window spectral pre-processing. This convolutional phase, previous to KPLS, is a viable alternative to the few available methods for finding the best mathematical pre-processing of the spectra, which is usually performed by trial and error. Analytical results concerning the calibration of selected analytes from partially selective spectra are employed to illustrate the performance of CKPLS. For this purpose, both simulated and experimental data sets have been employed, showing that automatic pre-processing of spectra is possible, with a success which is comparable to classical methods such as computing the spectral derivatives.