bluuebunny/crossref_metadata_2025_split huggingface dataset:
The construction of simultaneous optimal experimental designs for several polynomials in the calibration of analytical methods
Authors: Wolters R. , Kateman G. 
Published: May 2005

AbstractIn this paper a criterion is described for the construction of experimental designs for the evaluation of calibration models in analytical chemistry. The proposed criterion seeks a compromise between the D‐optimal designs for estimating the parameters of different polynomial models. A computer algorithm is presented for a sequential construction of experimental designs using the optimality criterion. The performance of the optimality criterion and the computer algorithm is elaborated for the problem of discrimination between a first‐ to a third‐degree polynomial for the calibration of analytical methods. An experimental design consisting of replicate measurements at five distinct levels equally spaced over the calibration range proved a good solution.
Data analysis in the shot noise limit. Part III: Adaptive data smoothing filters
Authors: Bialkowski Stephen E. 
Published: May 2005

AbstractDigital filter smoothing methods for shot‐noise‐limited data are addressed in this study. The preferred method is based on a Gaussian filter in which the width of the Gaussian filter function is varied depending on the estimate of the second derivative of the raw data. This filter is developed from the standpoint of maximum likelihood parameter estimation of the probability density function which describes shot‐noise‐limited data. The smoothing filter is tested and compared with the conventional sequential regression filter. This adaptive Gaussian smoothing filter works better than both the sequential regression and the adaptive Gaussian filter derived for normal noise. For data containing both high‐ and low‐frequency components, the limiting step in the adaptive filter is an estimation of the smoothing interval. Methods for determining an optimum smoothing interval are discussed. With the optimized smoothing interval, the adaptive Gaussian filter works well for data sets with a wide range of varying frequency components. In particular, synthetic data typical of atomic emission spectra are used to test this smoothing filter.
The use of a cross‐correlation technique to enhance Jansson's deconvolution procedure
Authors: Crilly Paul Benjamin 
Published: May 2005

AbstractThe use of a cross‐correlation prefiltering technique to enhance the ability of Jansson's iterative deconvolution procedure to deconvolve extremely noisy chromatographic data is investigated. Test cases include peaks whose resolutions are as low as 0.35 and whose signal‐to‐noise ratios are as low as 1:1. Evaluation criteria include RMS error, relative peak error and peak area repeatability. For comparison purposes, relative peak area errors and peak area variances are also evaluated for noisy but well resolved peaks that have only been prefiltered with the cross‐correlation filter. Jansson's method in conjunction with cross‐correlation prefiltering is shown not only to resolve overlapped peaks but in some cases to improve their signal‐to‐noise ratios. The study also establishes some limits to the capabilities of Jansson's method will regard to adverse data conditions.
The Free–Wilson paradigm redux: Significance of the Free–Wilson coefficients, insignificance of coefficient ‘uncertainities’ and statistical sins
Authors: Duewer David Lee 
Published: May 2005

AbstractThe Free–Wilson paradigm is an established and powerful tool for quantitatively relating activity with chemical structure. Current implementations of the paradigm, however, are flawed both conceptually and in execution. As part of an attempt to more fully realize the promise of the paradigm, it was necessary to examine these limitations in detail.This report introduces a robust, theory‐founded Free–Wilson implementation: stepwise principal components regression analysis (SPCRA). SPCRA is computationally superior to previous implementations but does not in itself correct their conceptual flaws.The development of SPCRA did, however, facilitate derivation of a simple and chemically significant interpretation of the Free–Wilson structure–activity model. A number of statistical aspects of this model commonly misused in previous applications are discussed at length. These discussions provide critical background for the development of an alternative implementation of the Free–Wilson paradigm.
Generalized simulated annealing for calibration sample selection from an existing set and orthogonalization of undesigned experiments
Authors: Kalivas John H. 
Published: May 2005

AbstractGeneralized simulated annealing (GSA) is an optimization procedure for locating the global optimum (maximum or minimum) of multidimenisonal continuous functions. GSA has been modified for optimization of discrete functions. Selection of calibration samples from an existing set defines discrete optimization and GSA is used to select optimal sets of calibration samples for specific analysis samples. The procedure is applied to near‐infrared spectra. When compared to using the complete set of 37 calibration samples, concentration prediction errors were reduced 50%–100% by using select sets of two to seven calibration samples. Additionally, GSA was able to improve a poorly designed experiment. GSA devised augmented experimental designs such that the overall experimental design (original plus augmented) was more orthogonal than the original.
Fuzzy multivariate rule‐building expert systems: Minimal neural networks
Authors: Harrington Peter B. 
Published: May 2005

AbstractA fuzzy multivariate rule‐building expert system (FuRES) has been devised which also functions as a minimal neural network. This system builds rules from training sets of data that use feature transformation in their antecedents. The rules are constructed using the ID3 algorithm with a fuzzy expression of classification entropy. The rules are optimal with respect to fuzziness and can accommodate overlapped and underlapped clusters of data. The FuRES algorithm combines the benefits obtained from simulated annealing and gradient optimization, which provide robustness and efficiency respectively. FuRES classification trees support OR logic in their inference. The system automatically generates meaningful and consistent certainty factors during rule construction. Unlike other neural networks, FuRES uses local processing which furnishes qualitative information in the rule structure of its classification trees and variable loadings of the weight vectors.
Multivariate analysis of 2D surfaces: Folding and interpretation
Authors: Alsberg Bjørn K. , Remseth Bjørn G. 
Published: May 2005

AbstractThe use of latent variable projection for analysis of non‐congruent 2D surfaces is presented. We give a formal description of the folding/unfolding process. A simulated 2D oscillator evolving in time is studied in detail to illustrate interpretation aspects of the method.
Resolution of strongly overlapping two‐way multicomponent data by means of heuristic evolving latent projections
Authors: Liang Yi‐Zeng , Kvalheim Olav M. , Rahmani Ali , Brereton Richard G. 
Published: May 2005

AbstractHigh‐performance liquid chromatography with diode array detection (HPLC––DAD) is used to characterize mixtures from chlorophyll a degradation experiments. Overlapping chromatographic peaks are resolved by means of the heuristic evolving latent projections (HELP) method. The HELP method is a self‐modelling curve resolution method. No assumptions are made about spectral and/or chromatographic peak shape. In the first step the method establishes the real noise level in the data by use of the so‐called zero‐component regions. This information is used to reveal selective chromatographic information and the number of chemical species at every retention time in unresolved chromatographic peaks. Utilising the selective chromatographic regions in combination with the zero‐concentration windows, unique resolution into concentration profiles and spectra of the pure chemical species is accomplished. HPLC–DAD data from six chlorophyll a degradation experiments were analysed. Consistent results were obtained even with very similar spectra for six or seven overlapping chemical components.
Eliminating complex eigenvectors and eigenvalues in multiway analyses using the direct trilinear decomposition method
Authors: Li Shousong , Gemperline Paul J. 
Published: May 2005

AbstractThe direct trilinear decomposition method (DTDM) is an algorithm for performing quantitative curve resolution of three‐dimensional data that follow the so‐called trilinear model, e.g. chromatography–spectroscopy or emission‐excitation fluorescence. Under certain coditions complex eigenvalues and eigenvectors emerge when the generalized eigenproblem is solved in DTDM. Previous publications never treated those cases. In this paper we show how similarity transformations can be used to eliminate the imaginary part of the complex eigenvalues and eigenvectors, thereby increasing the usefulness of DTDM in practical applications. The similarity transformation technique was first used by our laboratory to solve the similar problem in the generalized rank annihilation method (GRAM). Because unique elution profiles and spectra can be derived by using data matrices from three or more samples simultaneously, DTDM with similarity transformations is more efficient than GRAM in the case where there are many samples to be investigated.
A global perspective on multivariate calibration methods
Authors: Lang Patrick M. , Kalivas John H. 
Published: May 2005

AbstractThis paper consists of two distinct but related parts. In the first part a geometric theory of generalized inverses is presented and a methodology based on this theory is developed and applied to solve the K‐matrix and P‐matrix forms of Beer's law. It is shown that most currently accepted and practiced methods for solving these forms of Beer's law are just special cases of this geometric theory of generalized inverses. In addition, this geometric theory is used to explain why the current methods work and why they fail.In the second part a general methodology that includes as special cases least squares, principal component regression, partial least squares 1 and 2, continuum regression plus a variety of other described and undescribed methodologies is presented and then applied to solve the P‐matrix formulation of Beer's law. This general methodology, like the first, is also geometric in nature and relies on an understanding of projections.The main emphasis of this paper is one of perspective, which, if understood, provides the proper foundation for answering the general but extremely hard and possibly unanswerable question “what is the best method?”.
Application of orthogonal expansion to mapping and modelling
Authors: Cheng Zhaonian , Zhu Eryi , Chen Nianyi 
Published: May 2005

AbstractIn this paper we discuss the orthogonal expansion of data matrices and its application to mapping and modelling. Two new methods, modified optimal discriminant plane (MODP) for mapping and order Gram‐Schmidt orthogonalization (OGSO) for modelling, are proposed and examples are given.
Use of the Kalman filter for multivariate calibration in a real system and its comparison with CLS and pure component calibration methods
Authors: Péarez‐arribas L. V. , Navarro‐Villoslada F. , León‐Gonzalez M. E. , Polo‐Díez L. M. 
Published: May 2005

AbstractThe usefulness of the Kalman filter as an algorithm for calibration in a real system is shown. Results are compared with classical least squares and pure component calibration. The prediction of four priority pollutant chlorophenols in binary, ternary and quaternary mixtures was also carried out by Kalman filtering. The condition number, standard deviation and prediction error have been employed to choose the most suitable wavelength range. Comparison of the standard error of prediction in the validation set shows significant differences between the evaluated chlorophenols, the best results being obtained with Kalman multivariate calibration.
Determination of a multivariate detection limit and local chemical rank by designing a non‐parametric test from the zero‐component regions
Authors: Liang Yi‐Zeng , Kvalheim Olav M. , Höskuldsson Agnar 
Published: May 2005

AbstractIn this paper we redefine the term detection limit to embrace the inherent multivariate nature of samples, instrumental measurements and chemometrics resolution procedures. The so‐called zero‐component regions, i.e. parts with no chemical components eluting, are used as repeated analytical blanks to estimate a statistical multivariate detection limit for determining the number of chemical species in local regions of a single two‐way chromatogram or a collection of synchronized one‐way chromatograms. For two‐way chromatography the detection limit is determined from the distribution of the first eigenvalues obtained from all possible combinations of spectra in the zero‐component regions. The number of spectra in each calculation should correspond to the number included in the later examination of the local retention time regions. For one‐way chromatography on a collection of samples with similar chemical components at varying concentrations the same procedure is used, with the samples taking the role of the spectra in two‐way chromatography. The detection limit can be chosen at various confidence levels depending on whether false positive or negative detection of minor components is most critical. The results obtained from the zero‐eigenvalue distribution are more robust than those obtained by a previously developed F‐test.
Assessment of the effective rank of a (co)variance matrix: A non‐parametric goodness‐of‐fit test
Authors: Tomis̆ić Vladislav , Simeon Vladimir 
Published: May 2005

AbstractEach eigenvector of the dispersion matrix [X]T [X] was shown to be a partial predictor of the original data matrix [X], the sum of the predictions from the individual principal components being equal to the expectance of [X]. By comparing the distributions of the members of two neighbouring predicted matrices, [X̃]1…i and [X̃]1…i+1 (i.e. the sums of the first i and i + 1 individual predictions respectively), it was shown that they should be indistinguishable provided that i is equal to or greater than the effective rank of [X], and significantly different otherwise. This was confirmed by analysing the visible absorption spectra of methyl orange and methyl red solutions as well as the Raman spectra of Na2SO4 and MgSO4 solutions. On the grounds of these findings, a non‐parametric goodness‐of‐fit test for assessing the effective rank of [X] was proposed which proved to be comparatively conservative and more robust than most currently used tests.
Standard errors in the eigenvalues of a cross‐product matrix: Theory and applications
Authors: Faber N. M. , Buydens L. M. C. , Kateman G. 
Published: May 2005

AbstractNew expressions are derived for the standard errors in the eigenvalues of a cross‐product matrix by the method of error propagation. Cross‐product matrices frequently arise in multivariate data analysis, especially in principal component analysis (PCA). The derived standard errors account for the variability in the data as a result of measurement noise and are therefore essentially different from the standard errors developed in multivariate statistics. Those standard errors were derived in order to account for the finite number of observations on a fixed number of variables, the so‐called sampling error. They can be used for making inferences about the population eigenvalues. Making inferences about the population eigenvalues is often not the purposes of PCA in physical sciences. This is particularly true if the measurements are performed on an analytical instrument that produces two‐dimensional arrays for one chemical sample: the rows and columns of such a data matrix cannot be identified with observations on variables at all. However, PCA can still be used as a general data reduction technique, but now the effect of measurement noise on the standard errors in the eigenvalues has to be considered. The consequences for significance testing of the eigenvalues as well as the usefulness for error estimates for scores and loadings of PCA, multiple linear regression (MLR) and the generalized rank annihilation method (GRAM) are discussed. The adequacy of the derived expressions is tested by Monte Carlo simulations.
Generalized rank annihilation method. III: Practical implementation
Authors: Faber N. M. , Buydens L. M. C. , Kateman G. 
Published: May 2005

AbstractIn this paper we discuss the practical implementation of the generalized rank annihilation method (GRAM). The practical implementation comes down to developing a computer program where two critical steps can be distinguished: the construction of the factor space and the oblique rotation of the factors. The construction of the factor space is a least‐squares (LS) problem solved by singular value decomposition (SVD), whereas the rotation of the factors is brought about by solving an eigenvalue problem. In the past several formulations for GRAM have been published. The differences essentially come down to solving either a standard eigenvalue problem or a generalized eigenvalue problem. The first objective of this paper is to discuss the numerical stability of the algorithms resulting from these formulations. It is found that the generalized eigenvalue problem is only to be preferred if the construction of the factor space is not performed with maximum precision. This is demonstrated for the case where the dominant factors are calculated by the non‐linear iterative partial least‐squares (NIPALS) algorithm. Several performance measures are proposed to investigate the numerical accuracy of the computed solution. The previously derived bias and variance are proposed to estimate the number of physically significant digits in the computed solution. The second objective of this paper is to discuss the relevance of theoretical considerations for application of GRAM in the presence of model errors.
Classification of pyrolysis mass spectra of biological materials using convex cones
Authors: Mavrovouniotis Michael L. , Harper Alice M. , Ifarraguerri Agustin I. 
Published: May 2005

AbstractThis work addresses the classification of high‐dimensional time‐dependent pyrolysis mass spectra of biological samples. The aim was the detection and classification of biological agents, and the developed approach resembles mixture analysis. The data were projected on to a low‐dimensional subspace using singular value decomposition. Then a convex cone was formed on this subspace, showing as its corners physically meaningful components of the sample. This technique enabled separation of a biological material signal largely independent of the absolute amount of sample. The detection of the presence of any biological material could be accomplished based on the convex cone alone, without other reference to the mass spectra. Automated clustering of samples was successfully carried out using a minimal spanning tree.
Use of double windowing, variable selection, variable ranking and resolvability indices in window factor analysis
Authors: Brereton Richard G. , Elbergali Abdallah K. 
Published: May 2005

AbstractA method for selecting variables in the non‐sequential direction of a two‐way data matrix (e.g. wavelength in diode array HPLC) is described. Composition 1 and 2 resolvability indices are calculated according to the size of eigenvalues of uncentred data matrices as a window is moved along the sequential direction. A double‐window technique is then performed where resolvability indices are calculated as a window is moved along the non‐sequential direction. Some regions have higher resolvability indices and hence are more useful for resolution. Variables are ranked according to resolvability. Two simulations are analysed and it is shown that it is possible to obtain good resolution on a small subset of the original variables.
Mathematical approximation of sigmoidal shape curves tested on sensitometric curves of photographic material
Authors: Majer Jaroslav 
Published: May 2005

AbstractThis paper studies the application possibilities of various mathematical analytical functions to models of approximation of sigmoid sensitometric curves of photographic materials. The newly developed functions have been tested along with approximation functions taken from the literature: the former fulfil the statistical criteria of fitting the regression and experimental curve in the best way. The model functions can be used not only for objective determination of sensitometric quantities but also for determination of the general sensitivity (speed) of photographic materials.
Simple encoding of infrared spectra for pattern recognition. 1: Statistical examination of the effectiveness and information content by factor analysis
Authors: Schulz Henrik , Tetzlaff Klaus , Vogel Lydia 
Published: May 2005

AbstractThe spectral region from 700 to 3600 cm−1 is subdivided into several wave number intervals. The peaks in each interval are summarized by means of three encoding algorithms. Using a factor model of kcommon factors, the total extractable variacnce (com) of a given set of intervals is calculated and correlated with the redundancy of information in all these intervals. The value of com is verified by analysis of the factor loadings aik (factor pattern). Finally, the information content of some chosen sets of intervals coded by the three selected feature algorithms will be correlated to the probability of information flow through a serial‐parallel network. The encoding using only wave numbers was found to be the most effective.
Simulated‐annealing‐based optimization algorithms: Fundamentals and wavelength selection applications
Authors: Hörchner Uwe , Kalivas John H. 
Published: May 2005

AbstractSimulated annealing (SA) is a stochastic search method that has been applied to combinatorial search problems in chemometrics. Unlike strict iterative improvement methods, SA tolerates temporary moves to detrimental parameter configurations during an optimization. The method used by SA to decide whether or not to accept detrimental steps is a special case of a more general acceptance rule. The present work investigates the performance of various SA‐type algorithms that differ only in the acceptance rule for detrimental steps when optimizing continuous or discrete problems. A method for step width modulation is introduced to overcome the poor ability of SA type algorithms to locate the exact extreme of a function. The studied search strategies are modified for the discrete problem of wavelength selection. In order to evaluate SA‐type algorithms and their abilities to deal with the wavelength selection problem, two global measures of selectivity are used as criteria to determine the most suitable wavelength subset that maximizes selectivity for pure component ultraviolet–visible spectra.