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  • Analytical Chemistry and Spectroscopy  (11,708)
  • 1990-1994  (7,072)
  • 1980-1984  (4,318)
  • 1965-1969  (318)
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  • 101
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 102
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    Journal of Chemometrics 8 (1994), S. 102-102 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 103
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    Journal of Chemometrics 8 (1994), S. 111-125 
    ISSN: 0886-9383
    Keywords: PLS regression algorithm ; Kernel ; Many-variable data sets ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A fast PLS regression algorithm dealing with large data matrices with many variables (K) and fewer objects (N) is presented For such data matrices the classical algorithm is computer-intensive and memory-demanding. Recently, Lindgren et al. (J. Chemometrics, 7, 45-49 (1993)) developed a quick and efficient kernel algorithm for the case with many objects and few variables. The present paper is focused on the opposite case, i.e. many variables and fewer objects. A kernel algorithm is presented based on eigenvectors to the ‘kernel’ matrix XX TYYT, which is a square, non-symmetric matrix of size N × N, where N is the number of objects. Using the kernel matrix and the association matrices XXT (N × N) and YYT (N × N), it is possible to calculate all score and loading vectors and hence conduct a complete PLS regression including diagnostics such as R2. This is done without returning to the original data matrices X and Y. The algorithm is presented in equation form, with proofs of some new properties and as MATLAB code.
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  • 104
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    Journal of Chemometrics 8 (1994), S. 169-174 
    ISSN: 0886-9383
    Keywords: Kernel algorithm ; PLS ; SVD ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Lindgren et al. (J. Chemometrics, 7, 45-49 (1993)) published a so-called kernel algorithm for PLS regression of Y against X when the number of objects is very large. The algorithm is based solely on deflation of the cross-product matrices XTX, YTY and XTY. The algorithm is now described in a shorter and more transparent way and compared with a similar algorithm for the singular value decomposition of XTY.
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  • 105
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    Journal of Chemometrics 8 (1994) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 106
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    Journal of Chemometrics 8 (1994), S. 241-241 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 107
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    Journal of Chemometrics 8 (1994), S. 273-285 
    ISSN: 0886-9383
    Keywords: GRAM ; Least-squares problem ; Eigenvalue problem ; NIPALS ; Performance index ; Condition number ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In 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.
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  • 108
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    Journal of Chemometrics 8 (1994), S. 299-301 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 109
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    Journal of Chemometrics 8 (1994), S. i 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 110
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    Journal of Chemometrics 8 (1994), S. 349-363 
    ISSN: 0886-9383
    Keywords: Variable selection ; PLS ; Calibration ; Modelling ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A modified PLS algorithm is introduced with the goal of achieving improved prediction ability. The method, denoted IVS-PLS, is based on dimension-wise selective reweighting of single elements in the PLS weight vector w. Cross-validation, a criterion for the estimation of predictive quality, is used for guiding the selection procedure in the modelling stage. A threshold that controls the size of the selected values in w is put inside a cross-validation loop. This loop is repeated for each dimension and the results are interpreted graphically. The manipulation of w leads to rotation of the classical PLS solution. The results of IVS-PLS are different from simply selecting X-variables prior to modelling. The theory is explained and the algorithm is demonstrated for a simulated data set with 200 variables and 40 objects, representing a typical spectral calibration situation with four analytes. Improvements of up to 70% in external PRESS over the classical PLS algorithm are shown to be possible.
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  • 111
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    Journal of Chemometrics 8 (1994), S. i 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 112
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    Journal of Chemometrics 8 (1994), S. 409-421 
    ISSN: 0886-9383
    Keywords: Deconvolution ; FT-IR spectroscopy ; Protein conformations ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In a variety of spectroscopic techniques the fundamental problem exists of determination of the individual spectral components, intrinsically overlapped in the measured spectrum. This is a typical deconvolution problem and several methods and techniques have been proposed for its solution in the technical literature, but suggestions of new approaches are still of interest. A new deconvolution procedure is presented here based on the use of the conjugate gradient minimization algorithm with the addition of sutiable constraints directly obtained by the application to the measured spectrum of the second-derivative operator or more sophisticated resolution enhancement procedures. Since in the examined case deconvolution essentially requires the minimization of a non-convex function, the use of such constraints is extremely important to supply suitable input parameters to the conjugate gradient algorithm to avoid obtaining minimum points which have no physical meaning. In our case each spectral compoent used for deconvolution has been assumed to have a Gaussian analytical definition fully identified by three parameters (amplitude, central frequency, spectral bandwidth), so that the input values required to start the deconvolution process are the number M of Gaussian components and 3M suitable initial approximations of the parameters above. It is shown that all this information can be obtained from the measured data. The deconvolution procedure was implemented by a FORTRAN Microsoft Version 5.1 program and experimental results relative to spectroscopic data obtained by FT-IR analysis of human serum albumin are reported. The results are discussed and compared with data obtained by the use of other techniques.
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  • 113
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 114
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    Journal of Chemometrics 8 (1994), S. i 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 115
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    Journal of Chemometrics 5 (1991), S. 537-543 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 116
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    Journal of Chemometrics 6 (1992) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 117
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    Journal of Chemometrics 5 (1991), S. 523-536 
    ISSN: 0886-9383
    Keywords: Measurement errors ; Method comparison ; Mean square successive difference ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Comparison of methods is a technique often used for investigation of systematic errors of measurement methods. As concerns the design and analysis of such comparisons, much variety of opinion and practice exists. In one approach a few specimens are measured several times by different operators in different laboratories (reproducibility conditions) and in another approach several specimens are measured on one or a few occasions by one operator in the same laboratory (repeatability conditions). In this paper a model for the error structure of measurements is formulated and it is emphasized that one has to distinguish between two types of systematic errors: the first type depends only on the level of the measured quantity and the second type is specific for the separate specimens. On the basis of this model the information which can be obtained from the different designs of method comparisons is discussed. A new approach for the analysis of method comparisons with many specimens is also proposed.
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  • 118
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    Journal of Chemometrics 6 (1992), S. 29-40 
    ISSN: 0886-9383
    Keywords: Factor analysis ; Window factor analysis ; Multicomponent analysis ; Flow injection analysis ; Self-modeling curve resolution ; Bismuth chloride complexes ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Window factor analysis (WFA) is a self-modeling method for extracting the concentration profiles of individual components from evolutionary processes such as flow injection, chromatography, titrations and reaction kinetics. The method takes advantage of the fact that each component lies in a specific region along the evolutionary axis, called the window. Theoretical equations are derived. The method is used to extract the concentration profiles and spectra of seven bismuth species from data obtained by Gemperline and Hamilton, who injected bismuth perchlorate into a flowing stream of hydrochloric acid.
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  • 119
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    Journal of Chemometrics 6 (1992), S. 57-62 
    ISSN: 0886-9383
    Keywords: Closure ; Baseline ; Mean centering ; Rank ; Exploratory data analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper describes an investigation into the relationship of closure, a baseline offset and mean centering to the interpretation of matrix rank. The equivalence of a certain type of closure to a constant baseline (i.e. a simple numerical offset which may vary between response channels but is constant over all samples) is demonstrated. A systematic approach to the interpretation of the rank of a matrix is given.
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  • 120
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    Journal of Chemometrics 6 (1992), S. 97-102 
    ISSN: 0886-9383
    Keywords: Between-group variances ; Canonical variate criterion ; Eigenvalues ; Eigenvectors ; Orthogonal projection ; Within-group variance ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Canonical variate analysis is the appropriate descriptive technique for multivariate data which have an a priori group structure, but problems arise with this technique when there are more variables than within-group degrees of freedom because of singularity of matrices. In such cases it is shown through illustrative examples that principal component analysis is a viable substitute provided that the principal components are ranked according to the canonical variate criterion (ratio- of between- to within-group variances) rather than the usual criterion of total variance. This ranking can also be used to select components for subsequent discriminant analysis.
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  • 121
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    Journal of Chemometrics 6 (1992) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 122
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    Journal of Chemometrics 6 (1992), S. 119-133 
    ISSN: 0886-9383
    Keywords: Mass spectra ; Classification ; Structure description ; Fragmentation ; Ion series ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In order to investigate correlations between the functionality of compounds and the classification of their mass spectra, low-resolution spectra of monofunctional compounds have been classified by four supervised classification methods. The new classes are characterized by structural features and the correlation between functionality and classification is explained by fragmentation rules. Systematic misclassifications show that low-resolution mass spectra alone are not suitable for reliable identification of functionality.
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  • 123
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    Journal of Chemometrics 6 (1992), S. 163-175 
    ISSN: 0886-9383
    Keywords: Multiple-correspondence analysis ; Starch granule description ; Image analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Raw starch is composed botanically of characteristic granules of various sizes and shapes, so that each kind of starch may be characterized by the population of its granules. In the present study ten commercial starch species were studied: wheat, rice, manioc, potato, arrowroot, amylomaize, normal maize, waxy maize and two different banana species. Six variables measuring the size and shape of granules were obtained by image analysis. The objective was to find a method to describe and compare the granule populations of the ten species. For such a study, multiple-correspondence analysis (MCA) was applied. MCA makes it possible to draw similarity maps of categories and objects. For each starch species the frequency distributions (histograms) of the six variables were assessed and each granule was characterized by its species and the classes of histograms to which it belonged. MCA was applied to the granule table and a description of the histogram classes and the granules was obtained. From the variables description a general typology of the granules was deduced. The similarity maps showed considerable scatter of the granules for all species except rice. A particular species could therefore not be identified by a single granule, but the granule distribution seemed to be characteristic. MCA was an appropriate method to analyse these data because it points out non-linear relationships between quantitative and qualitative variables.
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  • 124
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    Journal of Chemometrics 6 (1992), S. 177-188 
    ISSN: 0886-9383
    Keywords: PLS ; Prediction error ; Background constituents ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A modification of a technique proposed by Lorber and Kowalski for the estimation of prediction errors is presented. The method is applied to five data sets. The results show that for some data sets the estimated prediction errors are close to the actual prediction errors for samples within the calibration range, while samples outside the calibration range must be background corrected before quantification of the prediction error.
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  • 125
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    Journal of Chemometrics 6 (1992), S. 189-198 
    ISSN: 0886-9383
    Keywords: Robust regression ; Partial least squares ; QSAR ; Perturbation study ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A robust partial least squares (PLS) regression algorithm is developed. This is achieved by substitution of the univariate regression steps in the iterative PLS2 algorithm by a robust alternative. The angle between loading vectors from both perturbed and unperturbed solutions is used as a measure of robustness. By means of a perturbation study on a structure-activity data set, it is demonstrated that the stability of the robust method is superior to standard PLS.
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  • 126
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 127
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    Journal of Chemometrics 6 (1992) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 128
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    Journal of Chemometrics 6 (1992), S. 267-281 
    ISSN: 0886-9383
    Keywords: Genetic algorithms ; Feature selection ; Multivariate analysis ; Optimization methods ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Genetic algorithms have been created as an optimization strategy to be used especially when complex response surfaces do not allow the use of better-known methods (simplex, experimental design techniques, etc.). This paper shows that these algorithms, conveniently modified, can also be a valuable tool in solving the feature selection problem. The subsets of variables selected by genetic algorithms are generally more efficient than those obtained by classical methods of feature selection, since they can produce a better result by using a lower number of features.
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  • 129
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    Journal of Chemometrics 7 (1993), S. 45-59 
    ISSN: 0886-9383
    Keywords: Partial least squares ; PLS algorithm ; Kernel ; Multivariate image analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A fast and memory-saving PLS regression algorithm for matrices with large numbers of objects is presented. It is called the kernel algorithm for PLS. Long (meaning having many objects, N) matrices X (N × K) and Y (N × M) are condensed into a small (K × K) square ‘kernel’ matrix XTYYTX of size equal to the number of X-variables. Using this kernel matrix XTYYTX together with the small covariance matrices XTX (K × K), XTY (K × M) and YTY (M × M), it is possible to estimate all necessary parameters for a complete PLS regression solution with some statistical diagnostics. The new developments are presented in equation form. A comparison of consumed floating point operations is given for the kernel and the classical PLS algorithm. As appendices, a condensed matrix algebra version of the kernel algorithm is given together with the MATLAB code.
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  • 130
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    Journal of Chemometrics 7 (1993), S. 77-88 
    ISSN: 0886-9383
    Keywords: Direct trilinear decomposition method ; Curve resolution ; Trilinear data ; Similarity transformation ; Generalized rank annihilation method ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The 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.
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  • 131
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    Journal of Chemometrics 7 (1993), S. 143-148 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 132
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    Journal of Chemometrics 7 (1993), S. 151-151 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 133
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    Journal of Chemometrics 7 (1993), S. 213-222 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Chemistry and Pharmacology
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  • 134
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    Journal of Chemometrics 7 (1993) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 135
    ISSN: 0886-9383
    Keywords: Multicomponent analysis ; Factor analysis ; Detection limit ; Local rank ; Zero-component region ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In 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.
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  • 136
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    Journal of Chemometrics 7 (1993), S. 447-452 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 137
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    Journal of Chemometrics 7 (1993), S. 477-494 
    ISSN: 0886-9383
    Keywords: Three-way principal components analysis ; Core matrix ; Body diagonalization ; Lower and upper bounds ; Simulation ; Soil contamination ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In contrast with conventional PCA, a direct superposition and joint interpretation of loading plots is not possible in three-way PCA, since there may be data variance which is described by unequal components of different modes. The contributions to variance of all possible combinations of components are described in the core matrix. Body diagonalization, which is achieved by appropriate rotation of component matrices, is an essential tool for simplifying the core matrix structure. The maximum degree of body diagonality which may be obtained from such transformations is analysed from both the mathematical and simulation viewpoints. It is shown that, at least in the average case, high degrees can be expected, which makes the procedure reasonable for many practical applications. Furthermore, simulation as well as theoretical derivation show that the success of body diagonality depends on the so-called polarity of the core array. The methodology is illustrated by a three-way data example from environmental chemistry.
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  • 138
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    Journal of Chemometrics 7 (1993), S. 551-557 
    ISSN: 0886-9383
    Keywords: Krylov sequence ; Partial least squares ; Polynomial regression ; Principal component regression ; R2 ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: PLS1 regression is generally viewed as lying in between PCR and OLS regression. Proof is given that the coefficient of determination, R2, for a PLS multivariate calibration model is at least as high as that for a PCR model with the same number of components. It appears that PLS can be linked to a correlation-weighted polynomial regression of a constant response on the eigenvalues of the covariance matrix of the predictor variables.
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    Journal of Chemometrics 8 (1994), S. 1-20 
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    Keywords: Discriminant analysis ; Least squares ; Prediction ; Regression ; Relationship ; Structure ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Twenty-two contrasting statistical methods are reviewed for their applicability to QSAR studies and similar prediction-oriented fields. Each method is concisely specified prior to explanatory or critical comment.
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  • 140
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    Journal of Chemometrics 8 (1994), S. 65-79 
    ISSN: 0886-9383
    Keywords: Genetic algorithms ; Full validation ; Feature selection ; Outlier detection ; Multivariate analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Genetic algorithms have been proved to be a very efficient method in the feature selection problem. However, as for every other method, if the validation of the results is performed in an incomplete way, erroneous conclusions can be drawn. In this paper a development of a previous genetic algorithm is presented so that a full validation of the results can be obtained. Furthermore, this algorithm has been shown to perform very well also as an outlier detector, allowing easy identification of the presence of outliers even in cases where the ‘classical’ techniques fail.
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  • 141
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    Journal of Chemometrics 4 (1990), S. 255-266 
    ISSN: 0886-9383
    Keywords: Similarity measure ; Cluster analysis ; Riemannian space ; Metric tensor ; Curvature ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The results of unsupervised pattern recognition methods are critically dependent on the measure of similarity used for clustering objects. There is little a priori information available on the relative utility of various similarity measures. We introduce here an alternative similarity measure based on the metric tensor measure (MTM). Two standard clustering strategies are tested with the proposed similarity measure: hierarchical clustering and the K-median method. As data we use the ARCH obsidian data, a data set on Hungarian coal, and trace element data on Hungarian paprika. Differences from the Mahalanobis distance measure are described for intraclass relations.
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  • 142
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    Journal of Chemometrics 8 (1994), S. 81-93 
    ISSN: 0886-9383
    Keywords: Sensory evaluation ; Cumulative ranks ; Assessor variation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A graphical method of assessing differences between sets of rankings based on cumulative ranks is developed. The method can be used to identify rankings that differ over all or just part of the range of objects ranked. The method is applied to an example of sensory evaluation of green peas in which ten assessors scored six attributes on each of 60 samples.
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    Journal of Chemometrics 4 (1990), S. i 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 144
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    Journal of Chemometrics 4 (1990), S. 271-289 
    ISSN: 0886-9383
    Keywords: Smoothing ; Digital filter ; Shot noise ; Signal processing ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Digital 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.
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    Journal of Chemometrics 4 (1990), S. 291-298 
    ISSN: 0886-9383
    Keywords: Deconvolution ; Jansson's method ; Peak restoration ; Iterative deconvolution ; Peak resolution ; Chromatographic deconvolution ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The 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.
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    Journal of Chemometrics 4 (1990), S. 299-321 
    ISSN: 0886-9383
    Keywords: Quantitative structure-activity relationships (QSARs) ; Free-Wilson ; Fujita-Ban Stepwise principal components regression analysis (SPCRA) ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The 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.
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    Journal of Chemometrics 4 (1990), S. 323-330 
    ISSN: 0886-9383
    Keywords: Target factor analysis ; Spectrophotometry ; Amino acids ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The UV spectra of mixture solutions consisting of tyrosine, tryptophane, phenylalanine, cystine, histidine and 3,4-dihydroxyl phenylalanine have been measured. The numbers, identities and concentrations of the amino acids in the mixtures have been determined successfully using target factor analysis. The effects of the wavelength range and the selected sampling interval on the results are discussed. Twenty-five synthetic mixture samples have been analysed successfully. The average recoveries are 98.9 for Tyr, 96.5 for Trp, 105.6 for Phe, 98.1 for Cys, 98.9 for His and 106.4 for Di-phe. The results obtained are in good agreement with those obtained by the Kalman filter method.
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    Journal of Chemometrics 4 (1990), S. 335-335 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 4 (1990), S. 331-334 
    ISSN: 0886-9383
    Keywords: Power method ; NIPALS algorithm ; Singular value decomposition ; Experimental design ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In a recent short communication, Miyashita et al. have commented on the weakness of the NIPALS algorithm (equivalently the power method) for calculating the eigenvalues out of order. They offer a diagnostic to ascertain when this may have occurred and suggested a modification to the NIPALS algorithm to avoid this situation. Further comments regarding the use of the power method and Miyashita's presentation of its weakness are warranted. The general inadequacies of methods for decomposing a matrix with degenerate eigenvalues and their relationship to the orthogonal design of experiments are discussed.
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    Journal of Chemometrics 8 (1994), S. i 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Chemistry and Pharmacology
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    Journal of Chemometrics 4 (1990), S. i 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 4 (1990), S. 337-354 
    ISSN: 0886-9383
    Keywords: Chemometrics ; Chemometrics Society ; History of chemometrics ; Pioneers of modern chemometrics ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This is a first foray into the historical start and early years of chemometrics from about 1972 onwards. We have gathered interviews with three originators (Kowalski, Wold and Massart) as well as with a selected group of six other well-known chemometricians who gradually became active in the 1970s (Christie, Clementi, Hopke, Martens, Brown and Deming). The interviews include amongst a host of subjective recollections a succinct record of the key historical literature as highlighted by the interviewees' own rankings of ‘earliest’ and ‘best’.A discussion of the most general commonalities in these interviews together with other historical material is presented in the second part of the paper.
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    Journal of Chemometrics 4 (1990), S. 355-360 
    ISSN: 0886-9383
    Keywords: Pattern recognition ; U.K. chemometrics usage ; Quantitative structure-activity relationships ; Artificial intelligence ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A survey of members of the U.K. QSAR Discussion Group has been made to determine the extent of use and development of chemometric and artificial intelligence (AI) methods in the analysis of multivariate quantitative structure-activity relationship (QSAR) data in the U.K. Chemometric methods were found to be well established in both industrial and educational establishments and there was significant method development occurring. AI methods were not employed to any great extent and the general level of interest in these techniques was low compared to chemometric methods. A requirement for more education in multivariate statistical methods and regression methods was indicated. A need for a user-friendly, comprehensive, commercially available multivariate statistical package containing multivariate stability testing and regression diagnostic methods was identified.
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    Journal of Chemometrics 4 (1990), S. 361-377 
    ISSN: 0886-9383
    Keywords: Abstract factor analysis ; Exploratory data analysis ; Principal components ; Simulated equilibria ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract factor analyses were performed on databases consisting of simulated samples from aqueous equilbria. The program COMPLEX was used to generate equilibrium species in a system of three reactant metals and five reactant bases. Reactant concentrations and pH were drawn from random-normal distributions so that sample data vectors comprised a multivariate log-normal distribution of equilibrium concentrations. In addition, sample groups were created containing different distributions for pH and reactant concentrations.Equilibrium species were shown to contain variance contributed by change in pH among samples as well as change in reactant concentrations. Factor modelling revealed the qualitative relationships among the species and how the relationships change with pH. Factors also revealed those reactants containing variance in the data matrix. In some cases, reactant variance obscured relationships between pH and the equilibrium species.Since factor modelling of a simulated data matrix revealed the expected chemical equilibrium interactions, a potentially powerful tool exists for investigating the effects of outliers and error.
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    Journal of Chemometrics 8 (1994), S. 305-331 
    ISSN: 0886-9383
    Keywords: Pyrolysis ; Mass spectroscopy ; Multivariate analysis ; Biological material identification ; Convexity ; Cones ; Subspaces ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This 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.
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    Journal of Chemometrics 4 (1990) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 8 (1994), S. 377-389 
    ISSN: 0886-9383
    Keywords: Kernel PLS regression ; Cross-validation ; Model dimensionality ; Multivariate image regression ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Multivariate images are very large data structures and any type of regression for their analysis is very computer-intensive. Kernel-based partial least squares (PLS) regression, presented in an earlier paper, makes the calculation phase more rapid and less demanding in computer memory. The present paper is a direct continuation of the first paper. In this study the kernel PLS algorithm is extended to include cross-validation for determination of the optimal model dimensionality. To show the applicability of the kernel algorithm, two examples from multivariate image analysis are used. The first example is an image from an airborne scanner of size 9 × 512 × 512. It consists of nine images which are regressed against a constructed dependent image to test the accuracy of the kernel algorithm when used on large data structures. The second example is a satellite image of size 7 × 512 × 512. Several different regression models are presented together with a comparison of their predictive capabilities. The regression models are also used as examples for showing the use of cross-validation.
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    Keywords: Principal components ; Multiple and stepwise regression ; Non-parametric density and regression estimation ; Bootstrap inference ; Canonical correlation ; PLS regression ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A statistical study of the dependence between various critical fusion temperatures of a certain kind of coal and its chemical components is carried out. As well as using classical dependence techniques (multiple, stepwise and PLS regression, principal components, canonical correlation, etc.) together with the corresponding inference on the parameters of interest, non-parametric regression and bootstrap inference are also performed.
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    Journal of Chemometrics 4 (1990), S. 441-441 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 5 (1991) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 5 (1991), S. i 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 5 (1991), S. 1-20 
    ISSN: 0886-9383
    Keywords: Averaging ; Median ; Outliers ; Regression ; Residuals ; Robustness ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this tutorial we first illustrate the effect of outliers on classical statistics such as the sample average. This motivates the use of robust techniques. For univariate data the sample median is a robust estimator of location, and the dispersion can also be estimated robustly. The resulting ‘z-scores’ are well suited to detect outliers. The sample median can be generalized to very large data sets, which is useful for robust ‘averaging’ of curves or images. For multivariate data a robust regression procedure is described. Its standardized residuals allow us to identify the outliers. Finally, a survey of related approaches is given. (This review overlaps with earlier work by the same author, which appeared elsewhere.)
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    Journal of Chemometrics 5 (1991), S. 21-35 
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    Keywords: Wronskian determinant ; Multicomponent systems ; Derivative spectroscopy ; Spline functions ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The use of Wronskian determinants in the study of multicomponent systems is proposed. The general theory is presented and applied to the spectrophotometric determination of the number of linearly independent components-absorbers. A detailed study of a two-component system is presented and analysed. Numerical methods for smoothing and differentiation of digitized spectra via cubic splines are used.
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    Journal of Chemometrics 5 (1991), S. 69-69 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 5 (1991), S. i 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 5 (1991), S. 71-71 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 5 (1991), S. 85-95 
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    Keywords: Deconvolution ; Gold's ratio ; Iterative deconvolution ; Chromatographic deconvolution ; Peak restoration ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper will consider the use of an iterative ratio technique called Gold's ratio method as an alternative to iterative constrained deconvolution methods for the restoration of overlapped and noisy chromatograpic peaks. The study will consist of first describing the technique and then evaluating its performance with respect to Jansson's deconvolution procedure. A Hewlett-Packard 5890A gas chromatograph will be used to generate most of the test data. The evaluation criteria will include convergence rates, peak area errors and variances, retention time variances and noise performance.
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    Journal of Chemometrics 5 (1991), S. 73-84 
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    Keywords: Optimization ; Technological process ; COMPLEX algorithm ; ANTICOMPLEX algorithm ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new program, named ANTICOMPLEX, has been specially written for searching the optimum conditions of a technological process. The algorithm is based on an iterative procedure with, at each step, a random sampling for a better exploration of the hyperspace of the parameters. Since the process is considered as a ‘black box’, the program operates by successive reductions of the variation domains with a strategy derived from some function optimization (COMPLEX). This approach is very flexible and the experimenter can stop the investigation at any series of experiments according to the desired accuracy for the optimum region. This program has been successfully tested on several real processes. This paper gives a complete description of the approach together with two illustrations on simulated processes.
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    Journal of Chemometrics 5 (1991), S. 113-116 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 5 (1991), S. 117-119 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 5 (1991), S. 97-111 
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    Keywords: Multivariate images ; Principal component regression ; Multivariate image regression ; Regression model ; Predicted image(s) ; Prediction quality scatter plot ; Visual diagnostic tools ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Regression between two blocks (usually called ‘dependent’ or Y and ‘independent’ or X) of data is a very important scientific and data-analytical tool. Regression on multivariate images is possible and constitutes a meaningful addition to existing univariate and multivariate techniques of image analysis. The regression can be used as a modeling tool or for prediction. The form of the regression equation chosen is dependent upon problem specification and information at hand. This paper describes the use of principal component regression (PCR). Both model building and prediction are presented for continuous Y-variables. The final goal is to supply new image material that can be used for visual inspection on a screen. Also, visual tools for diagnosis of model and prediction are provided, often based on derived image material. Examples of modeling and prediction are given for six channels in a seven-channel satellite image.
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 5 (1991), S. 121-128 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Chemistry and Pharmacology
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    Keywords: Derivatization reaction ; Factorial design ; Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Chemistry and Pharmacology
    Notes: A number of nucleophiles have been successfully identified and quantified using the Kröhnke reaction with 2,3-diphenyl derivatives of quinolizinium salts. Optimization of the reaction conditions by means of a mathematical model involving analysis of the response surface has led to a better understanding of the factors exerting an influence on the above reaction.The parameters chosen were temperature, reaction time, base concentration, water concentration and nucleophile concentration. The reaction was developed in polar aprotic solvents (acetone, acetonitrile). To facilitate the nucleophilic attack, the presence of an organic base (triethylamine) was necessary, although concentrations in excess of 0·15M did not alter the development of the reaction. Since pharmaceutical solutions are often aqueous, the influence of water on the reaction was studied. Low water volumes have no significant influence on the opening of the quinolizinium ring by the nucleophilic reagent. However, when the water proportion exceeded that of the organic solvent, the fluorescence intensity was lower than expected. Development of the fluorescent reaction product was first detected 5 min after the reaction started. The fluorescence intensity reached its optimum value after 138 min.
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  • 177
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    Journal of Chemometrics 6 (1992), S. i 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 178
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    Journal of Chemometrics 6 (1992), S. 85-96 
    ISSN: 0886-9383
    Keywords: Optimization ; Calibration ; Simulated annealing ; Experimental design ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper utilizes variable step size generalized simulated annealing (VSGSA) to design multicomponent calibration samples for spectroscopic data. VSGSA is an optimization procedure which is capable of converging to exact positions of global optima located on multidimensional continuous functions. On the basis of analysis sample response vectors, optimally designed calibration concentration matrices are obtained assuming knowledge of components present. The complexity of response surfaces established by the optimization criteria is described.
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  • 179
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    Journal of Chemometrics 6 (1992), S. 103-111 
    ISSN: 0886-9383
    Keywords: Mean centering ; Preprocessing ; Multivariate calibration ; Error propagation ; Principal component regression (PCR) ; Partial least squares (PLS) ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Traditionally, one form of preprocessing in multivariate calibration methods such as principal component regression and partial least squares is mean centering the independent variables (responses) and the dependent variables (concentrations). However, upon examination of the statistical issue of error propagation in multivariate calibration, it was found that mean centering is not advised for some data structures. In this paper it is shown that for response data which (i) vary linearly with concentration, (ii) have no baseline (when there is a component with a non-zero response that does not change in concentration) and (iii) have no closure in the concentrations (for each sample the concentrations of all components add to a constant, e.g. 100%) it is better not to mean center the calibration data. That is, the prediction errors as evaluated by a root mean square error statistic will be smaller for a model made with the raw data than a model made with mean-centered data. With simulated data relative improvements ranging from 1% to 13% were observed depending on the amount of error in the calibration concentrations and responses.
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  • 180
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 181
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    Journal of Chemometrics 6 (1992), S. 135-150 
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    Keywords: 2D surface ; Multivariate analysis ; Non-congruent ; Unfolding ; Folding ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The 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.
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  • 182
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    Journal of Chemometrics 4 (1990), S. 29-45 
    ISSN: 0886-9383
    Keywords: Tensor ; Superdiagonalization ; GRAM ; Three-way ; Multilinear ; Trilinear ; PARAFAC ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Modern instrumentation in chemistry routinely generates two-dimensional (second-order) arrays of data. Considering that most analyses need to compare several samples, the analyst ends up with a three-dimensional (third-order) array which is difficult to visualize or interpret with the conventional statistical tools.Some of these data arrays follow the so-called trilinear model, \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm R}_{ijk} = \sum\limits_{r = 1}^N {{\rm X}_{ir} {\rm Y}_{jr} {\rm Z}_{kr} + {\rm Error}_{ijk} } $$\end{document} These trilinear arrays of data are known to have unique factor analysis decompositions which correspond to the true physical factors that form the data, i.e. given the array ∝, a unique solution can be found in many cases for each order X, Y and Z. This is in contrast to the well-known second-order bilinear data factor analysis, where the abstract solutions obtained are not unique and at best cannot be easily compared with the underlying physical factors owing to a rotational ambiguity.Trilinear decompositions have had the disadvantage, however, that a non-linear optimization with many parameters is necessary to reach a least-squares solution. This paper will introduce a method for reducing the problem to a rectangular generalized eigenvalue-eigenvector equation where the eigenvectors are the contravariant form (pseudo-inverse) of the actual factors. It is shown that the method works well when the factors are linearly independent in at least two orders (e.g. Xir and Yjr are full rank matrices).Finally, it is shown how trilinear decompositions relate to multicomponent calibration, curve resolution and chemical analysis.
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  • 183
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 184
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    Journal of Chemometrics 6 (1992), S. 199-216 
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    Keywords: MARS ; Splines ; Multivariate calibration ; Non-linear ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This tutorial paper presents a simplified view of one of the more recently published multivariate calibration methods particularly suited to dealing with non-linear data sets. The method is referred to as MARS and stands for multivariate adaptive regression splines. Simple examples are provided to explain the workings of the method.
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    Journal of Chemometrics 6 (1992), S. 228-228 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 186
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    Journal of Chemometrics 6 (1992), S. 229-229 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 187
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    Journal of Chemometrics 6 (1992), S. 231-246 
    ISSN: 0886-9383
    Keywords: Integration methods ; Taylor series method ; Optimization methods ; Kinetic mechanisms ; Kinetic determinations ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A general equation to derive kinetic models up to any order is given. This equation greatly facilitates the application of the Taylor series method to the integration of kinetic models up to very high orders. When dealing with non-stiff models, computing time is always reduced by increasing the integration order, at least up to the 20th order. When the model is stiff, the integration order should be optimized; however, a twelfth order is recommended to integrate weakly stiff models. The use of an algorithm which permits the immediate calculation of the integration step size required to maintain a given accuracy leads to further reductions in computing time. When implemented as recommended here, a high-order Taylor series method is more rapid and accurate than Runge-Kutta and predictor-corrector methods and can be advantageously used in combination with optimization methods to perform mechanism studies and in multicomponent kinetic determinations.
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  • 188
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 189
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    Journal of Chemometrics 6 (1992), S. 289-305 
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    Keywords: Chemical structure database ; Conformational searching ; Similarity searching ; Substructure searching ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper presents a review of the rapid developments that have taken place over the last few years for the searching of databases of three-dimensional (3D) molecules. The geometric arrangement of the atoms in a 3D molecule is described by an interatomic distance matrix. This is a form of labelled graph that can thus be searched using the subgraph-isomorphism algorithms that are widely used for searching databases of two-dimensional (2D) molecules. Several in-house and commercial systems have been developed for 3D database searching that are based on such techniques. These systems are reviewed and their effectiveness demonstrated by examples of their use in the discovery of novel, biologically active molecules. Current systems represent a molecule by one or a small number of low-energy conformations and there is hence much interest in the development of representational techniques and searching algorithms that account for the full set of geometric arrangements that can be adopted by a flexible molecule.
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    Journal of Chemometrics 6 (1992) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 191
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    Keywords: GOLPE ; PLS ; Regression ; SDEP ; Variable selection ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A procedure called GOLPE is suggested in order to detect those variables which increase the predictivity of PLS models. The procedure is based on evaluating the predictive power of a number of PLS models built by different combinations of variables selected according to a factorial design strategy. Examples are given of the efficiency of this variable selection procedure, which shows how these predictive PLS models are better than those obtained by all variables and better than the corresponding ordinary regression models.
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  • 192
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    Journal of Chemometrics 7 (1993), S. 1-14 
    ISSN: 0886-9383
    Keywords: Continuum regression ; Dynamic model identification ; Principal component regression ; Partial least squares regression ; Finite impulse response ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The use of continuum regression (CR) for the identification of finite impulse response (FIR) dynamic models is investigated. CR encompasses the methods of principal component regression (PCR), partial least squares (PLS) and multiple linear regression (MLR). PCR and MLR are at the two extremes of the continuum. In PCR and PLS, cross-validation is used to determine the optimum number of factors or ‘latent variables’ to retain in the regression model. CR allows one to vary the method in addition. Cross-validation then determines both the optimum method and the number of latent variables. The CR ‘prediction error surface’ - a function of the method and number of latent variables - is elucidated. The optimal model is defined as the minimum of this surface. Among the cases studied, the optimal model usually comes from the region of the continuum between PCR and PLS. Few derive from the region between PLS and MLR. It is also demonstrated that FIR models identified by CR have frequency domain properties similar to those identified by PCR.
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    Journal of Chemometrics 7 (1993) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 4 (1990), S. 102-102 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 4 (1990) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 4 (1990), S. 102-102 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 197
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    Journal of Chemometrics 7 (1993), S. 117-130 
    ISSN: 0886-9383
    Keywords: Calibration ; Rank annihilation ; Three-way ; Trilinear ; Bilinear ; Non-bilinear ; Net analyte signal ; MS/MS ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Several multivariate methods are now available for the calibration of second-order or hyphenated instruments (e.g. GC/MS). When applied to bilinear data, it has been shown that calibration can be performed in the presence of unknown interferences - a significant advantage over first-order calibration. In this paper, non-bilinear rank annihilation (NBRA), a method which has the potential of handling, second-order non-bi-linear data, is studied through theoretical analysis and computer simulation. It is found that the second-order advantage can be carried over to non-bilinear data if a property defined as net analyte rank (NAR) holds for the analyte of interest. The net analyte signal (NAS) is defined accordingly for second-order calibration and the analogy to and difference from lower-order calibration are discussed. With NAS, some analytical figures of merit such as signal-to noise ratio, selectivity, sensitivity and limit of determination can be calculated for second order calibration. An application to MS/MS data is also given.
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 199
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    Journal of Chemometrics 7 (1993), S. 177-193 
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    Keywords: Multivariate analysis ; Function space ; Coefficient space ; B-splines ; Compression ; PCA ; PLS ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A general framework for manipulating spectra as functions in traditional multivariate methods such as PCA and PLS is described. The functional representation is very convenient for compression, ensuring smoothness and continuity. There are two fundamentally different types of representations: (a) by functions and (b) by function coefficients. The use of coefficients is the most practical way of analysis.
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