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  • Analytical Chemistry and Spectroscopy  (11,390)
  • 1990-1994  (7,072)
  • 1980-1984  (4,318)
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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 8 (1994), S. 263-272 
    ISSN: 0886-9383
    Keywords: Molecular descriptors ; Principal component analysis ; Chemometrics ; Pattern recognition ; Total surface area ; PCDD PCDF ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: New theoretical molecular indices are defined. They contain information about the whole molecular structure in terms of size, shape, symmetry and atom distribution. These indices are calcualted from the (x, y, z) co-ordinates of a molecule within different weighting schemes in a straightforward manner and represent a very general approach to describe molecules, molecular fragments, macromolecules and molecular conformations in a unitary conceptual framework. Their interpretability is quite evident and is defined by the same mathematical properties as the algorithm used for their calculation. Examples on the total surface area, toxicity of PCDD and PCDF and reaction rate of catalysed reactions show a high modelling power of these indices.
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  • 2
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    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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  • 3
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    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 8 (1994), S. 287-292 
    ISSN: 0886-9383
    Keywords: Rank annihilation ; Principal components ; Procrustes rotation ; Multivariate analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that the DATa ANalysis (DATAN) algorithm can be expressed in terms of rank annihilation factor analysis (RAFA). Subsequent advances in RAFA are applied to DATAN to eliminate the problems and restrictions associated with DATAN. The extension of DATAN in terms of the trilinear decomposition algorithm is discussed.
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  • 4
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    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 5 (1991), S. 68-69 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 5
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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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  • 6
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    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 4 (1990), 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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  • 7
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    New York, NY : Wiley-Blackwell
    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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  • 8
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    New York, NY : Wiley-Blackwell
    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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  • 9
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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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  • 10
    ISSN: 0886-9383
    Keywords: PCA ; Essential oils ; Mandarine ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Mandarine essential oils are extracted from green unripened fruits as well as from red fruits at ripening, both oils having specific uses as natural additives in the food industry. Two processes of production, pressing and peeling, are currently adopted in their production. Capillary gas chromatography with flame ionization detection has been suggested as a sensitive method for the fractionation of volatile components of the essential oils. Principal component analysis was proposed as an exploratory chemometric method for the differentiation of essential oils from fruits at different degrees of ripening, taking into account the processes of production. Product-moment correlations between variables (concentrations of 17 components) were used as starting matrices and the explained variance was adopted as a criterion for eigenvalue selection. Bi-plots and three-dimensional plots of unrotated principal component scores were systematically used as well as those of orthogonally rotated factor scores. The 17 variables were reduced to four principal components, which explained 87% of the total variance. Projection on the first three eigenvectors of all data as unrotated component scores allowed for a tentative differentiation of 59 oils according to their degree of ripening. The two processes of production were also differentiated in a sample of 55 oils.
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  • 11
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    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 4 (1990), S. 91-96 
    ISSN: 0886-9383
    Keywords: Sample size ; Monte Carlo ; Multivariate, normal ; Q-Q plots ; Classification ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Because many pattern recognition techniques are predicated on the assumption of mutivariate normal data, Monte Carlo simulation studies were performed to determine the number of samples that are necessary to describe a multivariate normal population adequately. From these studies we have learned that hundreds of samples are required. These results suggest that parametric procedures should only be used to analyze very large data sets.
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  • 12
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    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 5 (1991) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 13
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    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 4 (1990) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 14
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    Journal of Chemometrics 4 (1990), 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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  • 15
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    Journal of Chemometrics 4 (1990), 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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  • 16
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    Journal of Chemometrics 4 (1990), S. 97-100 
    ISSN: 0886-9383
    Keywords: Matrix decomposition ; NIPALS ; Principal component ; SIMCA ; PLS ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Non-linear Iterative Partial Least Squares (NIPALS) algorithm is used in principal component analysis to decompose a data matrix into score vectors and eigenvectors (loading vectors) plus a residual matrix. NIPALS starts with some guessed starting vector. The principal components obtained by NIPALS depends on the starting vector; the first principal component could not always be computed. Wold has suggested a starting vector for NIPALS, but we have found that even if this starting vector is used, the first principal component cannot be obtained in all cases. The reason why such a situation occurs is explained by the power method. A simple modification of the original NIPALS procedure to avoid getting smaller eigenvalues is presented.
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  • 17
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    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 5 (1991), S. 273-290 
    ISSN: 0886-9383
    Keywords: Correspondence analysis ; Eastern Lake Survey - Phase I data ; Acidic deposition ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Correspondence analysis (CA) was applied to lakewater data in order to study the effects of acidic deposition on the geochemical composition of lakes in the Adirondacks. The lake chemistry data analyzed were taken from the Eastern Lake Survey - Phase I (ELS-I) conducted by the U.S. Environmental Protection Agency. CA was used to identify ‘outlying’ lake samples as well as ‘superflous’ and ‘unresolved’ analytes. Correlational relationship among analytes were also examined.
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  • 18
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    Journal of Chemometrics 5 (1991), S. 299-308 
    ISSN: 0886-9383
    Keywords: Errors in variables ; Orthogonal regression ; Latent variables ; Acid rain ; Acidic deposition ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Techniques for testing for and estimating relative bias between two laboratories are developed and applied to a survey of the chemistry of streams in the United States. The design of the quality assurance program allows estimation of linear corrections for bias as well as testing of the hypothesis of linearity. Designs of this type are useful, but improvements are suggested.
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  • 19
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    Journal of Chemometrics 5 (1991), S. 291-298 
    ISSN: 0886-9383
    Keywords: Absorbance ratio ; Statistical confidence ; Quality control ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ratio measurements are commonly used to address a variety of analytical problems in environmental, forensic and pharmaceutical laboratories. In absorbance ratioing techniques, analytical chemists rely on the spectral features of the analyte(s) of interest. The absorbances at two wavelengths are monitored and the ratio of these two absorbances is computed. This ratio is then used to confirm the identity of the analyte(s) of interest, the purity of a product of the overlap of chromatographic peaks. These decisions often have far-reaching consequences (e.g. the identification of the source, biogenic or petrogenic, of hydrocarbons in biological tissues or water). Given the cost and the liabilities associated with such decisions, it is unfortunate that these ratios are seldom reported with any statistical confidence. The purpose of this study is to delineate the parameters that affect absorbance ratio measurements. The models that can be used to estimate the statistical confidence in these measurements are derived and evaluated experimentally. The results show that these models can estimate the relative standard deviations in absorbance ratios accurately. They can also estimate the effect of signal-to-noise ratio and the choice of wavelengths on the precision of absorbance ratios.
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  • 20
    ISSN: 0886-9383
    Keywords: Experimental design ; Binding ; Scatchard analysis ; Model ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The design of an experiment for the determination of binding parameters in the association between a ligand and a macromolecule with two groups of non-interacting binding sites is proposed. In the Gauss-Newton non-linear least squares treatment the standard deviation of each parameter is given as the product of two terms: one depending on the experimental error and the other, the diagonal element of the dispersion matrix, depending only on the independent variables of the system. In order to reach an optimal experimental design, these diagonal elements of the information matrix have to be minimized. In our approach this is achieved by searching those values of the independent variable which maximize the determinant of the information matrix. Furthermore, the limits of validity of the model are deduced from an analysis of the diagonal elements of the information matrix obtained under optimal conditions.
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  • 21
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    Journal of Chemometrics 5 (1991), S. 321-331 
    ISSN: 0886-9383
    Keywords: Screening ; Ground-water quality ; Monitoring ; Volatile organic compounds (VOCs) ; Optimization ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that the presence of 31-35 commonly measured volatile organic compounds (VOCs) in ground water can be detected with small error rates by using screening methods which analyze for a subset of such VOCs. A study of selected data sets indicates that analytical determinations of only from two to eight VOCs will suffice to detect 95% of all VOC hits. It is also shown that a serially optimal algorithm for selecting the VOCs for screening is very nearly as accurate as a globally optimal algorithm and much easier to implement. These conclusions are supported by empirical evidence from two drinking-water data sets and one hazardous waste site data set. Additional research areas are also outlined.
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  • 22
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    Journal of Chemometrics 5 (1991) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 23
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    Journal of Chemometrics 5 (1991), 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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  • 24
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    Journal of Chemometrics 5 (1991), S. 333-343 
    ISSN: 0886-9383
    Keywords: Rank estimation ; Bootstrap resampling ; Canonical correlation ; Excitation-emission matrix ; Singular value decomposition ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Rank estimation by canonical correlation analysis in multivariate statistics has been proposed as an alternative approach for estimating the number of components in a multicomponent mixture. A methodological turning point of this new approach is that it focuses on the difference in structure rather than in magnitude in characterizing the difference between the signal and the noise. This structural difference is quantified through the analysis of canonical correlation, which is a well-established data reduction technique in multivariate statistics. Unfortunately, there is a price to be paid for having this structural difference: at least two replicate data matrices are needed to carry out the analysis.In this paper we continue to explore the potential and to extend the scope of the canonical correlation technique. In particular, we propose a bootstrap resampling method which makes it possible to perform the canonical correlation analysis on a single data matrix. Since a robust estimator is introduced to make inference about the rank, the procedure may be applied to a wide range of data without any restriction on the noise distribution. Results from real as well as simulated mixture samples indicate that when used in conjunction with this resampling method, canonical correlation analysis of a single data matrix is equally efficient as of replicate data matrices.
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  • 25
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    Journal of Chemometrics 5 (1991), S. 345-360 
    ISSN: 0886-9383
    Keywords: Three-way PCA ; Three-way PLS ; PARAFAC ; Trilinear ; Unfolding ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For the calibration of chromatographic systems, different methods can be used. One class of methods utilizes three-way approaches. The calibration problem is stated in such a way that the decomposition of a three-way array can serve for the prediction of retention on new stationary phases.Two three-way approaches are presented: the Unfold-PCA and PARAFAC models. The theory of both methods is presented and the differences are highlighted, the main difference being that PARAFAC is a trilinear decomposition whereas Unfold-PCA is not. Both three-way methods are evaluated on a small data set consisting of retention measurements of eight solutes at six mobile phase compositions on six stationary phases. The differences in performance of the two models are minor.For calibration purposes, two variants of the methods are discussed: three-way PLS and an extension of PARAFAC. Again the theory and differences between the two methods are explained. The predictive performance of the two methods is compared using the same data set as earlier. The differences in predictive performance, however, are minor. Both methods are capable of predicting 98% of the variation in the test sets. Yet, there are other considerations when comparing methods than predictive performance, e.g. the quality of the predictions.
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  • 26
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    Journal of Chemometrics 5 (1991), S. 361-374 
    ISSN: 0886-9383
    Keywords: Closure ; Normalization ; Multivariate trimming ; Minimum distance ; Bootstrap ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Compositional data arise naturally in several branches of science, including chemistry, geology, biology, medicine, ecology and manufacturing design. In chemistry, these constrained data seem to occur typically when raw data are normalized or when output is obtained from a constrained estimation procedure, such as might be used in a source apportionment problem. It is important not only for chemists to be aware that the usual multivariate statistical techniques are not applicable to constrained data, but also to have access to appropriate techniques as they become available. The currently available methodology is due principally to Aitchison and is based on log-normal models. This paper suggests new parametric and non-parametric approaches to significantly improve the existing methodology. In the parametric setting, some recent work of Rayens and Srinivasan is extended and a practical regression model is proposed. In the development of the non-parametric approach, minimum distance methods coupled with multivariate bootstrap techniques are used to obtain point and region estimators.
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  • 27
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 28
    ISSN: 0886-9383
    Keywords: Principal component ; Cross-validation ; Selection of variables ; Residual ; Influential observation ; Procrustes analysis ; Chemometrics ; Wine analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Cross-validatory estimation of the bilinear model based on principal components is reviewed and Krzanowski's modification of Wold's procedure is described. Two different types of residuals useful for checking model adequacy are defined and indices measuring the influence of each observed unit on the estimates of the parameters are discussed. A method for the selection of variables derived from Procrustes analysis is described. Results arising from the study of two sets of enological data are given.
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  • 29
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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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  • 30
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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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  • 31
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    Journal of Chemometrics 6 (1992), S. 199-216 
    ISSN: 0886-9383
    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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  • 32
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    Journal of Chemometrics 5 (1991), S. 417-434 
    ISSN: 0886-9383
    Keywords: Factor analysis ; Power density distribution ; Chromatography ; Absorption spectroscopy ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Evaluation of the results of factor analysis of sets of spectroscopically detected chromatograms is carried out by examining the shapes of the abstract factors. This is done either by visual inspection or by analysis of the power density spectra produced from them. Owing to constraints imposed by the column function and the spectroscopic instrument function, the information content of the chromatograms necessarily occurs at low spatial frequencies. As a consequence, it appears as relatively broad features in the abstract chromatograms and as a peak in the low-frequency region of the corresponding power density plot. On the basis of examination of the power density distribution, a well-defined distinction is made between primary and secondary abstract factors. The major uncertainty encountered in determining the number of chemical components appears to arise from effects of contaminants in reagents.
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    Journal of Chemometrics 7 (1993), S. 153-163 
    ISSN: 0886-9383
    Keywords: Generalized inverse ; K-matrix analysis ; P-matrix analysis ; Least squares ; Principal component regression ; Partial least squares ; Continuum regression ; Beer's law ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This 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?”.
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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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    Journal of Chemometrics 6 (1992), S. 228-228 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 6 (1992) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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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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    Journal of Chemometrics 6 (1992), S. 247-255 
    ISSN: 0886-9383
    Keywords: Analysis of variance ; Assumptions ; Graphics ; Models ; Validation of model ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The computer has made it possible to scrutinize data rapidly by means of graphics. This should be done prior to the application of any model to the data, since the model must be validated before using it as a means of analyzing the data. The procedure is illustrated in terms of two examples of real experimental data.
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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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    Journal of Chemometrics 6 (1992), S. 257-266 
    ISSN: 0886-9383
    Keywords: Principal factor analysis ; Factor analysis ; Eigenvalue analysis ; Multivariate analysis ; Weighted factor analysis ; Procrustean analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Two approximate methods for weighted principal components analysis (WPCA) were devised and tested in numerical experiments using either empirical variances (obtained from replicated data) or assumed variances (derived from unreplicated data). In the first (‘spherical’) approximation each data vector was assigned a weight proportional to the geometrical mean of its variances in all dimensions. The arithmetical mean of variances was used instead in the other approximation. Both the numerical experiments with artificial data containing random errors of various kinds (constant, proportional, constant plus proportional, Poisson) and the analysis of two sets of Raman spectra clearly indicated the necessity of introducing statistical weights. The spherical approximation was found to be slightly better than the arithmetical one. The application of statistical weighting was found to improve the performance of PCA in estimation problems.
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    Journal of Chemometrics 6 (1992), S. 267-281 
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    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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    Journal of Chemometrics 6 (1992) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 7 (1993), S. 99-115 
    ISSN: 0886-9383
    Keywords: Classification ; Appreciation function ; Regularized discriminant analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Chemistry and Pharmacology
    Notes: Regularized discriminant analysis has proven to be a most effective classifier for problems where traditional classifiers fail because of a lack of sufficient training samples, as is often the case in highdimensional settings. However, it has been shown that the model selection procedure of regularized discriminant analysis, determining the degree of regularization, has some deficiencies associated with it. We propose a modified model selection procedure base on a new appreciation function. By means of an extensive simulation it was shown that the new model selection procedure performs better than the original one. We also propose that one of the control parameters of regularized discriminant analysis be allowed to take on negative values. This extension leads to an improved performance in certain situations. The results are confirmed using two chemical data sets.
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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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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 6 (1992) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 6 (1992), S. 11-28 
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    Keywords: Three-way PLS ; PARAFAC ; Unfolding ; Validatory tools ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The methods PARAFAC and three-way PLS are compared with respect to their ability to predict reversed-phase retention values. Special attention is paid to simple validatory tools, the meaning and use of which are explained.
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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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    Journal of Chemometrics 8 (1994), S. 293-294 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 7 (1993), S. 527-541 
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    Keywords: Principal component analysis ; Projection pursuit ; Simulated annealing algorithm ; Robust statistics ; Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Chemistry and Pharmacology
    Notes: Principal component analysis (PCA) is a widely used technique in chemometrics. The classical PCA method is, unfortunately, non-robust, since the variance is adopted as the objective function. In this paper, projection pursuit (PP) is used to carry out PCA with a criterion which is more robust than the variance. In addition, the generalized simulated annealing (GSA) algorithm is introduced as an optimization procedure in the process of PP calculation to guarantee the global optimum. The results for simulated data sets show that PCA via PP is resistant to the deviation of the error distribution from the normal one. The method is especially recommended for use in cases with possible outlier(s) existing in the data.
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    Journal of Chemometrics 8 (1994), S. 301-302 
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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 8 (1994), S. 303-303 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 6 (1992), S. 63-64 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 6 (1992), S. 65-83 
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    Keywords: Trilinear decomposition ; Receptor modeling ; Source identification ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In many cases, monitoring data for ambient airborne particles can be organized in the form of a three-way data table with one way for chemical species, one for sampling periods and one for sites. A direct trilinear decomposition followed by a matrix reconstruction (DTDMR) is developed to analyze such a data table as a whole. The three-way data set is composed into three two-way matrices by a direct trilinear decomposition (DTD). The column vectors of each of the matrices are called ‘source profiles’, ‘emission patterns’ and ‘site coefficients’ respectively. Particulate sources are identified by examining both their source profiles and emission patterns. After the sources have been identified, emission patterns and site coefficients are used to produce a three-way matrix that gives estimates of mass contributions of sources to the samples collected at every site in every period. By simulation study, not only has the method been verified, but a good indicator has been found that shows the number of factors (i.e. sources) in the system. Unlike other receptor models, DTDMR does not require source profile data and does not involve trial-and-error procedures. Since DTDMR identifies sources based on variations in two dimensions, it has a higher potential to distinguish two sources that have similar chemical compositions. The DTDMR model has provided excellent results with simulated data and has been applied in a real world three-way data set.
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    Journal of Chemometrics 6 (1992), S. 85-96 
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    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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    Journal of Chemometrics 6 (1992), S. 97-102 
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    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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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 8 (1994), S. 111-125 
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    Keywords: PLS regression algorithm ; Kernel ; Many-variable data sets ; Chemistry ; Analytical Chemistry and Spectroscopy
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    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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    Journal of Chemometrics 8 (1994), S. 375-376 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Journal of Chemometrics 8 (1994), S. 377-389 
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    Keywords: Kernel PLS regression ; Cross-validation ; Model dimensionality ; Multivariate image regression ; Chemistry ; Analytical Chemistry and Spectroscopy
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    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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    Journal of Chemometrics 8 (1994), S. 102-102 
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    Journal of Chemometrics 8 (1994), S. 179-180 
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    Journal of Chemometrics 8 (1994), S. 181-203 
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    Keywords: RAFA ; GRAM ; Eigenvalues ; Bias ; Variance ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Rank annihilation factor analysis (RAFA) is a method for multicomponent calibration using two data matrices simultaneously, one for the unknown and one for the calibration sample. In its most general form, the generalized rank annihilation method (GRAM), an eigenvalue problem has to be solved. In this second paper expressions are derived for predicting the bias and variance in the eigenvalues of GRAM. These expressions are built on the analogies between a reformulation of the eigenvalue problem and the prediction equations of univariate and multivariate calibration. The error analysis will also be performed for Lorber's formulation of RAFA. It will be demonstrated that, depending on the size of the eigenvalue, large differences in performance must be expected. A bias correction technique is proposed that effectively eliminates the bias if the error in the bias estimate is not too large. The derived expressions are evaluated by Monte Carlo simulations. It is shown that the predictions are satisfactory up to the limit of detection. The results are not sensitive to an incorrect choice of the dimension of the factor space.
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    Keywords: Fitting ; Non-linear ; Least squares ; Refinement ; Constraints ; MSE ; Confidence ; C ls ; XPS ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A non-linear least squares iterative refinement has been implemented which shows high performance on a multiple-peak spectrum including baseline or background. Constraints as well as links within a range are introduced to drive the mathematical optimization: each peak parameter (i.e. height, position, Gaussian/Lorentzian mixing ratio and HWHM on both left and right sides) has assigned to it an allowed range of variation and can be strained to be correlated with other parameters belonging either to the same peak (symmetrical peaks) or to other peaks (doublets, triplets, etc.). Peak shapes typical of XP spectra are used and applications in the field of XPS are discussed. Through emulated curves with Poisson distributed noise, the accuracy and precision of back-calculated (refined) parameters have been estimated. Moreover, a confidence level calculated from X2 and degrees of freedom has been suggested to check the overall fitting of experimental curves where the signal-to-noise ratio is a priori unknown. An application to real C ls XP spectra is described as an example and a list of suggestions is given to match operator requirements. Finally, features of NLLSRC are discussed with respect to other approaches.
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    Journal of Chemometrics 8 (1994) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Chemistry and Pharmacology
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  • 77
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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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  • 78
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    Journal of Chemometrics 8 (1994), S. 243-243 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 79
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    Journal of Chemometrics 8 (1994), S. 245-261 
    ISSN: 0886-9383
    Keywords: Factor analysis ; Spectral resolution ; Two-dimensional luminescence ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A factor analysis algorithm that estimates the spectra of mixture components using the set of most dissimilar rows and/or columns is described and illustrated. This algorithm uses the distance as a measure of spectral similarity and is suitable for application to a variety of the bilinear matrix-formatted data types produced by hyphenated and multidimensional analytical techniqes. The algorithm requires that the data matrix contain at least one row or column that corresponds to the pure spectrum of each component to effect accurate spectral resolution. The performance of the method is illustrated using the resolution of excitation and emission spectra of up to four components from experimental fluorescence excitation-emission matrices (EEMs). In the case of the EEM, characteristic bands in an emission spectrum effect resolution of the excitation spectrum of the corresponding component, while characteristic bands in an excitation spectrum lead to resolution of the corresponding emission spectrum. The use of the set of most dissimilar rows and columns to evaluate the degree of overlap in the component spectra and compare the quality of row and column solutions is also described.
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  • 80
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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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  • 81
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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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  • 82
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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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    Topics: Chemistry and Pharmacology
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  • 83
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    Journal of Chemometrics 4 (1990) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Chemistry and Pharmacology
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  • 84
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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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  • 85
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    Journal of Chemometrics 4 (1990), S. 47-50 
    ISSN: 0886-9383
    Keywords: Classification ; Pattern recognition ; Preprocessing ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Over the past 15 years the linear learning machine has been applied to a large number of chemical problems. The learning machine approach is conceptually simple and does not require knowledge about the statistical distribution of the data. However, there are problems associated with this approach. One problem which has not been investigated is the influence of mislabeled samples on the positioning of the hyperplane in feature space. If a few samples in a data set are incorrectly tagged prior to training (i.e. the samples are labeled as members of class 2 even though they are actually members of class 1), it is still possible using the linear learning machine to achieve a classification success rate of 100% for the training set. However, unfavorable results will be obtained for the prediction set. The magnitude of this effect and its potential implications regarding the proper use of the linear learning machine are discussed.
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  • 86
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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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    Topics: Chemistry and Pharmacology
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  • 87
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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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    Topics: Chemistry and Pharmacology
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  • 88
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    Journal of Chemometrics 5 (1991), S. 73-84 
    ISSN: 0886-9383
    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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  • 90
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    Journal of Chemometrics 5 (1991), S. 85-95 
    ISSN: 0886-9383
    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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  • 91
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    Journal of Chemometrics 5 (1991), S. 97-111 
    ISSN: 0886-9383
    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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  • 92
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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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    Topics: Chemistry and Pharmacology
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  • 93
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    Journal of Chemometrics 5 (1991), S. 263-271 
    ISSN: 0886-9383
    Keywords: Mean ; Variance ; Lognormal ; Optimal estimators ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Theoretical and simulation results are employed to evaluate mean and variance estimates for normal data when a lognormal distribution is assumed and for lognormal data when a normal distribution is assumed. Misspecifying the distribution leads to the use of suboptimal estimation methods. However, the results show that the suboptimal methods still produce estimators of good quality (low bias and variance) relative to the minimum variance unbiased estimators for each distribution, at least when practical efficiency is considered.
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  • 94
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    Journal of Chemometrics 4 (1990), S. 389-412 
    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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  • 95
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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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    Topics: Chemistry and Pharmacology
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  • 96
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    Keywords: Discriminant analysis ; Size-exclusion chromatography ; Wheat proteins ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Continuous digitalized signals such as spectra, electrophoregrams or chromatograms generally have a large number of data points and contain redundant information. It is therefore troublesome performing discriminant analysis without any preliminary selection of variables. A procedure for the application of canonical discriminant analysis (CDA) on this kind of data is studied. CDA can be presented as a succession of two principal component analyses (PCAs). The first is performed directly on the raw data and gives PC scores. The second is applied on the gravity centres of each qualitative group assessed on the normalized PC scores. A stepwise procedure for selection of the relevant PC scores is presented. The method has been tested on an illustrative collection of 165 size-exclusion high-performance (SE-HPLC) chromatograms of proteins of wheat belonging to 55 genotypes and grown in three locations. The discrimination of the growing locations was performed using seven to nine PC scores and gave more than 86% accurate classifications of the samples both in the training sets and the verification sets. The genotypes were also rather well identified, with more than 85% of the samples correctly classified. The studied method gives a way of assessing relevant mathematical distances between digitalized signals according to qualitative knowledge of the samples.
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  • 97
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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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  • 98
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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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  • 100
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    Journal of Chemometrics 5 (1991), S. 37-48 
    ISSN: 0886-9383
    Keywords: Optimization ; Simulated annealing ; Calibration ; Experimental design ; Multicomponent analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Generalized 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.
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