摘要:

AbstractOne of the major applications of factor analysis in the chemical literature, self‐modeling curve resolution (SMCR), is covered in this review, including a historical account of the methods derived from Lawton and Sylvestre's original method. Papers treating the theory or applications of SMCR are included. Qualitative and quantitative applications are described where appropriat

ISSN:0886-9383    

DOI:10.1002/cem.1180040103

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractFluorescence lifetime provides a third independent dimension of information for the resolution of total luminescence spectra of multicomponent mixtures. The incorporation of this parameter into the excitation–emission matrix (EEM) by the phase modulation technique results in a three‐dimensional excitation–emission–frequency array (EEFA). Multicomponent analysis based on the three‐dimensional EEFA brings a qualitative change for the resolved spectra, i.e. individual spectra can be uniquely resolved, which is impossible with any two‐dimensional analysis. In this paper we present a method for analyzing the EEFA. We show mathematically that with the three‐dimensional analysis of the EEFA individual spectra and lifetimes can be obtained. Our algorithm is developed in mathematical detail and is demonstrated by its application to a two‐co

ISSN:0886-9383    

DOI:10.1002/cem.1180040104

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractModern 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‐calledtrilinearmodel,\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 ℝ, a unique solution can be found in many cases for each orderX,YandZ. 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.XirandYjrare full rank matrices).Finally, it is shown how trilinear decompositions relate to multicomponent calibration, curve resolutio

ISSN:0886-9383    

DOI:10.1002/cem.1180040105

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractOver 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.

ISSN:0886-9383    

DOI:10.1002/cem.1180040106

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractIn previous papers Jansson's method was found to be successful at deconvolving severely overlapped gas chromatographic peaks. In the most recent paper the method was evaluated with respect to quantitative accuracy, peak area and retention time repeatability. The problems associated with deconvolving noisy data and some alternatives which can improve the ability of Jansson's method to deconvolve noisy data are discussed. These alternatives include presmoothing the data with a nine‐point, third‐order polynomial filter and data reblurring. This paper will test these methods on peaks with various degrees of resolution and signal‐to‐noise

ISSN:0886-9383    

DOI:10.1002/cem.1180040107

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractIn the series of analytical techniques for identification of chemical substances, infrared spectrometry presents by far the highest information content. However, the information is most complicated too. It concerns a multitude of band positions, band intensities and band shapes, which, moreover, can be disturbed by matrix and other effects. The high redundancy, however, allows conclusions to be made by a qualitative, subjective procedure.IR is often used to prove the equality between a sample and a reference material, e.g. in quality control of a production process. In forensic control, the question to be answered is mostly not to prove equality, but whether or not the presence of a compound in a sample, e.g. a drug, can be proved. Moreover, testing has to be performed according to objective rules.To fulfil these requirements, a new retrieval algorithm, the ‘Adequate Peaks Search’, is presented. It concerns representing the reference spectra by sets of adequate peak positions and the sample spectrum by a set of all peak positions, whereafter the cross‐sections of the sample set and the reference sets are determined. The concept ‘adequate peak’ is defined and criteria have been formulated to evaluate the results into a positive (presence of the analyte is proved) or negative (presence is not proved) conclusion.The detection limit when the Adequate Peaks Search (APS) method was applied was four to seven times lower than that attained by a number o

ISSN:0886-9383    

DOI:10.1002/cem.1180040108

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractWhen using hyphenated methods in analytical chemistry, the data obtained for each sample are given as a matrix. When a regression equation is set up between an unknown sample (a matrix) and a calibration set (a stack of matrices), the residual is a matrixR.The regression equation is usually solved by minimizing the sum of squares ofR. If the sample contains some constituent not calibrated for, this approach is not valid. In this paper an algorithm is presented which partitionsRinto one matrix of low rank corresponding to the unknown constituents, and one random noise matrix to which the least squares restrictions are applied. Properties and possible applications of the algorithm are also discussed.In Part 2 of this work an example from HPLC with diode array detection is presented and the results are compared with generalized rank annihilation factor analysis (GRAFA).

ISSN:0886-9383    

DOI:10.1002/cem.1180040109

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractBecause 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.

ISSN:0886-9383    

DOI:10.1002/cem.1180040110

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe 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 presente

ISSN:0886-9383    

DOI:10.1002/cem.1180040111

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180040112

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY