Harald Martens

Variable selection in near infrared spectroscopy based on significance testing in partial least squares regression

A jack-knife based method for variable selection in partial least squares regression is presented. The method is based on significance tests of model parameters, in this paper applied to regression coefficients. The method is tested on a near infrared (NIR) spectral data set recorded on beer samples, correlated to extract concentration and compared to other methods with known merit. The results show that the jack-knife based variable selection performs as well or better than other variable selection methods do. Furthermore, results show that the method is robust towards various cross-validation schemes (the number of segments and how they are chosen).

A multivariate calibration problem in analytical chemistry solved by partial least-squares models in latent variables

Abstract The use of partial least squares in latent variables (PLS) for multivariate calibration problems is described. The application is the simultaneous determination of ligninsulfonate, humic acid and an optical whitener, from their severely overlapping fluorescence spectra. The predictive performance of the resulting calibration model is tested with a separate set of samples. The PLS method also identifies samples which do not fit the calibration model. The PLS method is compared with principal components analysis combined with multiple regression.

Comparison of prediction methods for multicollinear data

In this paper we discuss the partial least squares (PLS) prediction method. The method is compared to the predictor based on principal component regression (PCR). Both theoretical considerations and computations on artificial and real data are presented.

Extended Multiplicative Signal Correction as a Tool for Separation and Characterization of Physical and Chemical Information in Fourier Transform Infrared Microscopy Images of Cryo-sections of Beef Loin

Extended multiplicative signal correction (EMSC) is used to separate and to characterize physical and chemical information in spectra from Fourier transform infrared (FT-IR) microscopy. This appears especially useful for applications in infrared spectroscopy where the scatter variance in spectra changes with the chemical variance in the sample set. In these cases the chemical information of specific bands that are assigned to functional groups is easier to interpret when the scatter information is removed from the spectra. We show that scatter (physical) information in FT-IR spectra of heat-treated beef loin is related to chemical changes due to heat treatment. This information is caused by textural changes induced by the heat treatment and expressed by physical effects as the optical path length. The chemical absorbance changes introduced in the FT-IR spectra due to heat treatment are shifts in the protein region of the infrared spectrum caused by changes in the secondary structure of the proteins. If the scatter and the chemical information is not separated properly, scatter information may erroneously be interpreted as chemical information.

Thermal stability of fatty acid-serum albumin complexes studied by differential scanning calorimetry

Differential scanning calorimetry has been used to study the thermal stability of bovine serum albumin as affected by binding of fatty acids (lauric acid and stearic acid) and sodium dodecyl sulfate (SDS). All the ligands stabilized the protein molecules in a similar manner, but to different levels. A maximum increase in denaturation temperature of 30 degrees C was obtained with lauric acid. The thermograms indicate the presence of several ligand-albumin complexes having different heat stabilities. Variations in pH in 0.9% NaCl affected the heat stability of both ligand-poor and ligand-rich albumin, the former being more sensitive to variations in pH within the physiological range. Variations in NaCl concentration affected the thermal stabilities at neutral pH, expecially at low salt concentrations. While ligand-rich albumin was somewhat destabilized by increasing NaCl concentrations, ligand-poor albumin was strongly stabilized. The potential use of differential scanning calorimetry in ligand-albumin research is discussed.

Multivariate calibration. II: Chemometric methods

Abstract In this outline of new approaches to multivariate calibration in chemistry the following topics are treated: Advantages of multivariate calibration over conventional univariate calibration: detect and eliminate selectivity problems. Multivariate calibration methods based on selection of some variables vs. methods based on data compression of all the variables. Direct vs. indirect calibration: pure constituents or known samples for calibration? Calibration methods based on data compression by physical modelling: Beers law. Use of Beers law in controlled and natural calibration: the generalized least-squares fit and the best linear predictor. Extending Beers law to handle unknown selectivity problems. Calibration methods based on data compression by factor modelling: the principal component regression and partial least-squares regression. Methods for detecting abnormal samples (outliers). Pre-treatments to linearize data.

Factor analysis of chemical mixtures: Non-negative Factor Solutions for Spectra of Cereal Amino Acids

Abstract From spectral data for a set of mixtures of unknown compounds, the spectra and the amounts of the pure components can be estimated without physical separation of the compounds. Spectra for the amino acid content of whole finger millet grain samples are used as the example. Different methods of factor analysis and weighting were compared. The number of relevant “pure components” (i.e. protein groups) was found to be 3 in finger millet grain grown under widely varying fertilizer conditions. Ranges of acceptable spectra of these “pure components” and ranges of their amounts were found by applying non-negativity criteria to the factor analysis solutions. The spectra were then estimated concisely by performing the factor analysis on the data scaled to different units in which all components except one remained constant and were excluded from the factor solution in turn. The amounts of the three “pure components” were estimated by multiple regression. Thus the rotationally ambiguous factor analysis solution was converted to a physically meaningful description of the unknown compounds in the mixtures.

Restricted Least Squares Estimation of the Spectra and Concentration of Two Unknown Constituents Available in Mixtures

The problem considered is the identification of two unknown chemical compounds and the estimation of their proportions in a set of unknown mixtures of the two compounds, given data that are vectors of measurements on their mixtures. It is assumed that the expected value of a mixture vector is an unknown convex linear combination of two unknown component vectors and least squares estimation is used to obtain a set of possible solutions of the mixing proportions and the component vectors. Obtaining a unique solution requires additional constraints or information. The solution set is interpreted geometrically and examples involving amino acids and light absorbance data are given.

Sensory profiling data studied by partial least squares regression

Abstract The statistical analysis of a descriptive sensory profiling data set distributed at the sensometrics meeting is presented. The data set is analysed with focus on the sensory differences between products (cooked potatoes). The data analytical strategy involves a descriptive statistical analysis to obtain an overview of the distribution and standard deviations of the scores for each sensory attribute. Subsequently, three-way analysis of variance (AVOVA) of the data gives a statistical measure of the reliability of the sensory attributes supplemented by principal component analysis, which visualise the main tendencies of systematic variation. Discriminant and ANOVA partial least squares regressions are used to relate the sensory structure to product design structure and vice versa. Statistical reliability and predictive validity of the product differences are obtained by ANOVA and cross-validation. Similar data structures are observed in the various multivariate models. Texture, taste and flavour attributes differentiated the potato samples, with the texture attributes being most reliable. It is emphasised that an appropriate interpretation of the profiling data should also include knowledge of the experimental background.

Simultaneous determination of five different food proteins by high-performance liquid chromatography and partial least-squares multivariate calibration

Abstract A method is described for the simultaneous determination of food proteins originating from different raw food materials. The proteins are hydrolysed to amino acids which are labelled with dansyl chloride and finally separated by reversed-phase high-performance liquid chromatography. Partial least-squares multivariate calibration is used to resolve and quantify the overlapping amino-acid patterns. The method enables muscle protein, collagen, soy protein (both texturate and isolate), casein and milk protein to be quantified in both heated and raw samples from the same calibration set. The accuracies for the raw and heated samples averaged 3% and 6% relative total protein content, respectively.