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  • 1
    Electronic Resource
    Electronic Resource
    Residual bilinearization. Part 1: Theory and algorithms (1990)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 4 (1990), S. 79-90 
    Details
    ISSN: 0886-9383
    Keywords: PLS ; Three-way matrices ; Calibration ; Residual bilinearization ; Background correction ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: When 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 matrix R.The regression equation is usually solved by minimizing the sum of squares of R. If the sample contains some constituent not calibrated for, this approach is not valid. In this paper an algorithm is presented which partitions R into 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).
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180040109
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Interactive variable selection (IVS) for PLS. Part 1: Theory and algorithms (1994)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 8 (1994), S. 349-363 
    Details
    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.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180080505
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A PLS kernel algorithm for data sets with many variables and few objects. Part II: Cross-validation, missing data and examples (1995)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 9 (1995), S. 459-470 
    Details
    ISSN: 0886-9383
    Keywords: PLS ; kernel algorithm ; multivariate calibration ; EM algorithm ; cross-validation ; missing data ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This is Part II of a series concerning the PLS kernel algorithm for data sets with many variables and few objects. Here the issues of cross-validation and missing data are investigated. Both partial and full crossvalidation are evaluated in terms of predictive residuals and speed and are illustrated on real examples. Two related approaches to the solution of the missing data problem are presented. One is a full EM algorithm and the second a reduced EM algorithm which applies when the number of missing values is small. The two examples are multivariate calibration data sets. The first set consists of UV-visible data measured on mixtures of four metal ions. The second example consists of FT-IR measurements on mixtures consisting of four different organic substances.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180090604
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Multi-way principal components-and PLS-analysisA preliminary version of this paper was presented at the Nordic Symposium for Applied Statistics, RECKU, Copenhagen, January 1986. (1987)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 1 (1987), S. 41-56 
    Details
    ISSN: 0886-9383
    Keywords: Multi-way array ; Multiorder array ; Principal components ; PLS ; Multivariate calibration ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Lohmöller-Wold decomposition of multi-way (three-way, four-way, etc.) data arrays is combined with the non-linear partial least squares (NIPALS) algorithms to provide multi-way solutions of principal components analysis (PCA) and partial least squares modelling in latent variables (PLS).The decomposition of a multi-way array is developed as the product of a score vector and a loading array, where the score vectors have the same properties as those of ordinary two-way PCA and PLS. In image analysis, the array would instead be decomposed as the product of a loading vector and an image score matrix.The resulting methods are equivalent to the method of unfolding a multi-way array to a two-way matrix followed by ordinary PCA or PLS analysis. This automatically proves the eigenvector and least squares properties of the multi-way PCA and PLS methods.The methodology is presented; the algorithms are outlined and illustrated with a small chemical example.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180010107
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Residual bilinearization. Part 2: Application to HPLC - diode array data and comparison with rank annihilation factor analysis (1990)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 4 (1990), S. 135-146 
    Details
    ISSN: 0886-9383
    Keywords: PLS ; Three-way matrices ; Calibration ; Residual bilinearization ; Background correction ; GRAFA ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The partial least squares-residual bilinearization (PLS-RBL) approach to background correction presented in Part 1 of this work is demonstrated with an example from HPLC with diode array detection. Data are also evaluated with generalized rank annihilation factor analysis (GRAFA) and results are compared.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180040205
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    Paper (German National Licenses)
    Fulltext
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