W. Penninckx

Comparison of regularized discriminant analysis linear discriminant analysis and quadratic discriminant analysis applied to NIR data

Three classifiers, namely linear discriminant analysis (LDA), quadratic discriminant analysis (QDA) and regularized discriminant analysis (RDA) are considered in this study for classification based on NIR data. Because NIR data sets are severely ill-conditioned, the three methods cannot be directly applied. A feature selection method was used to reduce the data dimensionality, and the selected features were used as the input of the classifiers. RDA can be considered as an intermediate method between LDA and QDA, and in several cases, RDA reduces to either LDA or QDA depending on which is better. In some other cases, RDA is somewhat better. However, optimization is time consuming. It is therefore concluded that in many cases, LDA or QDA should be recommended for practical use, depending on the characteristics of the data. However, in those cases where even small gains in classification quality are important, the application of RDA might be useful.

Validation of the calibration procedure in atomic absorption spectrometric methods

A general strategy for the validation of the calibration procedure in AAS was developed. In order to accomplish this, the suitability of different experimental designs and statistical tests, to trace outliers, to examine the behaviour of the variance and to detect a lack-of-fit, was evaluated. Parametric as well as randomization tests were considered. For these investigations, simulated data were used, which are based on real measurements. The results obtained indicate that to validate a straight-line model, the measurement points should preferably be distributed over three or four concentration levels. In order to check the goodness-of-fit, the significance of the quadratic term should be investigated. A lack-of-fit to a second degree model is better detected when the measurement points are distributed over more than four concentration levels. For an unweighted second degree model, an analysis of variance (ANOVA) lack-of-fit can be used, while a randomization test is proposed for a weighted model. A one-tailed F-test or an alternative randomization test should be used to trace a non-constant variance.

Detection of bias in method comparison by regression analysis

Abstract Regression analysis is often applied to validate a newly developed method against a reference method. The present work investigates the risk of not detecting a systematic difference between two analytical methods (=β-error) and determines the number of points needed to detect a bias with a specified β-error. Approximate formulae are proposed to predict the sample size required to detect from a regression analysis a proportional or a constant bias, i.e. a bias in the slope or in the intercept. These results are compared with those of computer simulations. Three different designs to distribute the data are studied, namely, a normal and a rectangular distribution over the whole measurement range as well as an experimental design where the measurements are performed at three fixed concentration levels. For a known straight line relationship, it is demonstrated that this last design is to be preferred. A procedure is also proposed to simultaneously test slope and intercept of the orthogonal least-squares line. It is shown that, for a given number of data, an evaluation based on such a joint test allows a more reliable bias detection.

Feature reduction by Fourier transform in pattern recognition of NIR data

A Fourier transform (FT) was used as a tool to reduce the number of variables in pattern recognition of NIR data. Five procedures were designed to select the FT coefficients as the input of the classifier of regularized discriminant analysis (RDA). 11 data sets were analysed and the results were also compared with other dimensionality reduction methods of Principal component analysis (PCA) and univariate feature selection method. Our results demonstrate that FT is a fast and powerful feature reduction method and that its results are comparable to those of PCA as a feature reduction method before classification. It has the additional advantage that feature reduction is applied to individual spectra instead of to a set of spectra, as in the case of PCA.

Effectiveness of palladium chemical modification for the determination of cadmium by graphite furnace atomic absorption spectrometry

The effect of palladium on the cadmium absorbance signal was investigated. To reduce the background absorbance due to sodium chloride, large amounts of palladium should be avoided. A combination of 6 µg of palladium and 500 µg of ammonium nitrate allows the direct determination of cadmium in undiluted urine against aqueous standards. The detection limit (3σ) was calculated to be 0.1 µg l–1. This mixed modifier is shown also to be applicable to the analysis of milk and blood with a detection limit of 0.5 µg l–1.

Effectiveness of palladium as a chemical modifier for the determination of lead in biological materials and foodstuffs by graphite furnace atomic absorption spectrometry

SummaryA combination of 6 μg palladium and 15 μg magnesium nitrate is proposed as chemical modifier for lead determinations in biological materials and foodstuffs. The applicability of this modifier was investigated by the analysis of several types of samples, as compared to the classical NH4H2PO4 and Mg(NO3)2 modifier. Direct determinations of lead against aqueous standard solutions can be performed in 3-fold diluted urine, 2-fold diluted milk and 6-fold diluted blood, when the proposed modifier is added. A method for lead determinations in potatoes using the combined palladium and magnesium nitrate modifier, after a microwave acid digestion, is described. The optimum GFAAS pyrolysis temperature remains dependent on the matrix and should be determined for each type of sample. A wider linear range of the calibration curve is observed when the proposed Pd modifier is used.

Detection, interpretation and correction of changes in the instrumental response of near-infrared monochromator instruments over time

Abstract A new approach is proposed for the detection of changes in the instrumental response of near-infrared spectrometers over time. This approach is based on simulating possible instrumental differences and performing a principal component analysis of the simulated data set. This multivariate approach is tested on a real near-infrared data set and the results are compared to those obtained by the several univariate diagnostic procedures commonly used to check the stability of the response of a nearinfrared spectrometer over time. Advantages and drawbacks of this new approach are discussed. A simulated data set is used to study the influence of using different types of standards on the results obtained by this approach.

Knowledge-based computer system for the detection of matrix interferences in atomic absorption spectrometric methods

A knowledge-based computer system which assists with the detection of matrix interferences during the validation of atomic absorption spectrometry (AAS) is described. The system compares the slopes of a standard addition line and an aqueous calibration line. An experimental design is proposed which guarantees that the probability of not detecting important interferences (β-error) is acceptably low. To permit a detection of interferences by the comparison of curved calibration lines, a linearization is proposed. The system is developed in a Windows environment and is one module of a more complete hypertext system for the final validation of AAS methods.

A knowledge-based system for the selection of dissolution methods prior to the atomic absorption analysis of drugs

Abstract The knowledge about the selection of dissolution methods prior to the atomic absorption analysis of drugs available in an analytical industrial laboratory was structured in a number of rules, which were subsequently transformed into a decision tree. The nature of the sample was found to be the principal parameter determining the selection of the dissolution method, while in some situations a distinction had to be made according to the type of analyte, the concentration of the analyte or the purpose of the analysis. The suitability of three tools which permit the presentation of this knowledge in a computer system was investigated. The application built with ToolBook software, a hypertext language for the personal computer, was found to be the most suitable, due to its attractive user interface, ease of implementation and the possibility given to the user to add his personal comments. The rule-based expert system and self-generating decision tree proved to be less suitable alternatives.

Hypertext tools for the selection of dissolution methods prior to the atomic absorption analysis of pharmaca

Abstract A hypertext system for the selection of dissolution methods prior to the atomic absorption analysis of pharmaca was developed. The knowledge about dissolution methods, available in an industrial quality assurance laboratory, was first structured in a decision tree. The tree was implemented in a knowledge-based computer system using Toolbook software, an object oriented language for the personal computer. Beside its user-friendliness and possibility to build an attractive user-interface, this language permits the extension of the system with some important options, which would be difficult or impossible to create with other tools. The most important options are: (a) a partial maintainability of the system that is given to the user, (b) the visualization of the strategy of the decision making by displaying the structure of the tree in combination with a list of consulted pages, and (c) a database which ensures the completeness of the presented information and can easily be separately consulted.