Sample-Specific Prediction Error Measures in Spectroscopy

Near-Infrared Spectroscopy Coupled with Chemometrics and Artificial Neural Network Modeling for Prediction of Emulsion Droplet Diameters

There is increased interest in the food industry for emulsions as delivery systems to preserve the stability of sensitive biocompounds with the aim of improving their bioavailability, solubility, and stability; maintaining their texture; and controlling their release. Emulsification in continuously operated microscale devices enables the production of emulsions of controllable droplet sizes and reduces the amount of emulsifier and time consumption, while NIR, as a nondestructive, noninvasive, fast, and efficient technique, represents an interesting aspect for emulsion investigation. The aim of this work was to predict the average Feret droplet diameter of oil-in-water and oil-in-aqueous mint extract emulsions prepared in a continuously operated microfluidic device with different emulsifiers (PEG 1500, PEG 6000, and PEG 20,000) based on the combination of near-infrared (NIR) spectra with chemometrics (principal component analysis (PCA) and partial least-squares (PLS) regression) and artificial neural network (ANN) modeling. PCA score plots for average preprocessed NIR spectra show the specific grouping of the samples into three groups according to the emulsifier used, while the PCA analysis of the emulsion samples with different emulsifiers showed the specific grouping of the samples based on the amount of emulsifier used. The developed PLS models had higher R² values for oil-in-water emulsions, ranging from 0.6863 to 0.9692 for calibration, 0.5617 to 0.8740 for validation, and 0.4618 to 0.8692 for prediction, than oil-in-aqueous mint extract emulsions, with R² values that were in range of 0.8109-0.8934 for calibration, 0.5017-0.6620, for validation and 0.5587-0.7234 for prediction. Better results were obtained for the developed nonlinear ANN models, which showed R² values in the range of 0.9428-0.9917 for training, 0.8515-0.9294 for testing, and 0.7377-0.8533 for the validation of oil-in-water emulsions, while for oil-in-aqueous mint extract emulsions R² values were higher, in the range of 0.9516-0.9996 for training, 0.9311-0.9994 for testing, and 0.8113-0.9995 for validation.

Orthogonality constrained inverse regression to improve model selectivity and analyte predictions from vibrational spectroscopic measurements

In analytical chemistry spectroscopy is attractive for high-throughput quantification, which often relies on inverse regression, like partial least squares regression. Due to a multivariate nature of spectroscopic measurements an analyte can be quantified in presence of interferences. However, if the model is not fully selective against interferences, analyte predictions may be biased. The degree of model selectivity against an interferent is defined by the inner relation between the regression vector and the pure interfering signal. If the regression vector is orthogonal to the signal, this inner relation equals zero and the model is fully selective. The degree of model selectivity largely depends on calibration data quality. Strong correlations may deteriorate calibration data resulting in poorly selective models. We show this using a fructose-maltose model system. Furthermore, we modify the NIPALS algorithm to improve model selectivity when calibration data are deteriorated. This modification is done by incorporating a projection matrix into the algorithm, which constrains regression vector estimation to the null-space of known interfering signals. This way known interfering signals are handled, while unknown signals are accounted for by latent variables. We test the modified algorithm and compare it to the conventional NIPALS algorithm using both simulated and industrial process data. The industrial process data consist of mid-infrared measurements obtained on mixtures of beta-lactoglobulin (analyte of interest), and alpha-lactalbumin and caseinoglycomacropeptide (interfering species). The root mean squared error of beta-lactoglobulin (% w/w) predictions of a test set was 0.92 and 0.33 when applying the conventional and the modified NIPALS algorithm, respectively. Our modification of the algorithm returns simpler models with improved selectivity and analyte predictions. This paper shows how known interfering signals may be utilized in a direct fashion, while benefitting from a latent variable approach. The modified algorithm can be viewed as a fusion between ordinary least squares regression and partial least squares regression and may be very useful when knowledge of some (but not all) interfering species is available.