Rolf Manne

Analysis of two partial-least-squares algorithms for multivariate calibration

Abstract Manne, R., 1987. Analysis of two partial-least-squares algorithms for multivariate calibration. Chemometrics and Intelligent Laboratory Systems , 2: 187-197. Two algorithms for multivariate calibration are analysed in terms of standard linear regression theory. The matrix inversion problem of linear regression is shown to be solved by transformations to a bidiagonal form in PLS1 and to a triangular form in PLS2. PLS1 gives results identical with the bidiagonalization algorithm by Golub and Kahan, similar to the method of conjugate gradients. The general efficiency of the algorithms is discussed.

Subwindow factor analysis

Abstract The method of subwindow factor analysis (SFA) is introduced as a solution to the problem of directly extracting component spectra from overlapping structures obtained from hyphenated chromatography without first resolving concentration profiles. This is of advantage when a complete resolution cannot be obtained or is of less interest in the analytical situation. The method is based upon comparisons of chromatographic regions (subwindows) which have only one eluting component in common. The paper presents the theory and an application to a structure with 4 overlapping components from a data set from a mixture of polyaromatic hydrocarbons recorded by high-performance liquid chromatography diode array detection (HPLC-DAD).

MISSING VALUES IN PRINCIPAL COMPONENT ANALYSIS

Abstract Calculation schemes for principal component analysis are considered for the case when some matrix elements are missing. Iterative solutions are proposed—either a set of multilinear regression problems or as singular-value decomposition problems with iterative imputation of missing values. If mean values are subtracted from the data matrix, they should also be included in the iteration scheme. Test calculations using Matlab show that the regression approach is somewhat faster than the imputation approach. The results with a substantial amount of missing data are different and superior to those obtained with the naive NIPALS algorithm in common use in chemometrics.

A new procedure for Roothaan's symmetry-restricted open-shell SCF method

Roothaans symmetry-restricted open-shell SCF method is derived without the use of lagrangian multipliers for a general case of one open shell per symmetry. A single Fock operator is formulated converging to the same eigenfunctions and eigenvalues as obtained by the standard double- eigenvalue method of Roothaan. Comparisons are made with other formulations of the method, and test calculations are provided for singly and doubly ionized states of methane in the neutral ground-state geometry.

White, grey and black multicomponent systems: a classification of mixture problems and methods for their quantitative analysis

Abstract “Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry … If mathematical analysis should ever hold a prominent place in chemistry — an aberration which is happily almost impossible — it would cause a rapid and widespread degeneration of that science.” Auguste Comte, Philosophie Positive (1830) Liang, Y.-Z., Kvalheim, O.M. and Manne, R., 1993. White, grey and black multicomponent systems. A classification of mixture problems and methods for their quantitative analysis. Chemometrics and Intelligent Laboratory Systems, 18: 235–250. Multivariate calibration and resolution methods for handling samples of chemical mixtures are examined from the point of view of the analytical chemist. The methods are classified concordant to three different kinds of analytical mixture systems; i.e. ‘white’, ‘grey’, and ‘black’ analytical systems. Advantages and limitations of available multivariate calibration and resolution methods are discussed with respect to the proposed classification of the analytical mixture problem.

Configuration interaction calculations of satellite structure in photoelectron spectra of H2O

Abstract Configuration interaction wavefunctions were computed for the satellite peaks in the core and the valence photoelectron spectra of H 2 O. Relative intensities were computed in the sudden approximation including electron correlation in the neutral ground state. The intensity profile of the O 1s ESCA spectrum is understood in terms of single excitations from the 3a 1 and the 1b 1 orbitals to low lying virtual MOs. Strong correlation effects are observed for the levels in the inner valence region where the satellites derive their intensity both from the 2a 1 and 3a 1 MOs.

Resolution of two-way data from hyphenated chromatography by means of elementary matrix transformations

Abstract Data from mixtures studied by hyphenated chromatography, e.g., HPLC-DAD and similar techniques, are resolved into spectra and concentration profiles by an iterative technique using elementary matrix transformations. Applications are made to one artificial data set and three sets previously analyzed in the literature. The technique is very fast and seems to perform at least as well as those previously developed, but requires less intervention from the user.

Use of convexity for finding pure variables in two-way data from mixtures

Abstract The principles for finding pure (or key) variables in two-way non-negative data from mixtures are discussed. It is shown that with a normalization to constant projection on a given vector one obtains a convex and bounded representation of the data with the pure variables as extreme points. An algorithm based upon this observation is compared with other methods for the same purpose and tested using data from the literature.

Local resolution of hyphenated chromatographic data

Abstract Subwindow factor analysis (SFA), a new local resolution method, is applied to the resolution of the target analyte in strongly overlapping chromatographic peaks. Making full use of information hidden in overlapping regions, SFA successfully resolved the spectrum of the analyte of interest. Orthogonal projection is then used to obtain the corresponding chromatographic profile. The separation ability of chromatography is greatly enhanced with this local resolution method. It can be directly used for the qualitative and quantitative analysis of the target analytes for the hyphenated two-way chromatographic data. The geometrical meaning implied in this procedure is also discussed. Real and simulated examples are given to illustrate the efficiency of the proposed method.

The morphological score and its application to chemical rank determination

Abstract Most spectra with structural information are smooth. Making use of this feature, a new procedure is proposed for automatic chemical rank determination. In order to avoid accumulation of noise, key spectra instead of the full matrix are analyzed in the procedure. A simplified morphological factor, morphological score (MS), is proposed. The noise level of morphological analysis is established with the help of F -test. The proposed procedure was successfully applied in the study of self-association behavior of alcohol. Results show that two classes of aggregates contribute to near infrared (NIR) spectra besides the monomer. Data sets produced by other techniques were also tested.