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  • 1
    ISSN: 1573-9023
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0886-9383
    Keywords: PLS regression algorithm ; Kernel ; Many-variable data sets ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A fast PLS regression algorithm dealing with large data matrices with many variables (K) and fewer objects (N) is presented For such data matrices the classical algorithm is computer-intensive and memory-demanding. Recently, Lindgren et al. (J. Chemometrics, 7, 45-49 (1993)) developed a quick and efficient kernel algorithm for the case with many objects and few variables. The present paper is focused on the opposite case, i.e. many variables and fewer objects. A kernel algorithm is presented based on eigenvectors to the ‘kernel’ matrix XX TYYT, which is a square, non-symmetric matrix of size N × N, where N is the number of objects. Using the kernel matrix and the association matrices XXT (N × N) and YYT (N × N), it is possible to calculate all score and loading vectors and hence conduct a complete PLS regression including diagnostics such as R2. This is done without returning to the original data matrices X and Y. The algorithm is presented in equation form, with proofs of some new properties and as MATLAB code.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 8 (1994), S. 99-100 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 7 (1993), S. 45-59 
    ISSN: 0886-9383
    Keywords: Partial least squares ; PLS algorithm ; Kernel ; Multivariate image analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A fast and memory-saving PLS regression algorithm for matrices with large numbers of objects is presented. It is called the kernel algorithm for PLS. Long (meaning having many objects, N) matrices X (N × K) and Y (N × M) are condensed into a small (K × K) square ‘kernel’ matrix XTYYTX of size equal to the number of X-variables. Using this kernel matrix XTYYTX together with the small covariance matrices XTX (K × K), XTY (K × M) and YTY (M × M), it is possible to estimate all necessary parameters for a complete PLS regression solution with some statistical diagnostics. The new developments are presented in equation form. A comparison of consumed floating point operations is given for the kernel and the classical PLS algorithm. As appendices, a condensed matrix algebra version of the kernel algorithm is given together with the MATLAB code.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 5
    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
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  • 6
    ISSN: 0886-9383
    Keywords: partial least squares (PLS) ; variable selection ; IVS-PLS ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: With the aim of developing PLS models with improved predictive properties, an interactive variable selection (IVS) approach for PLS regression was introduced in Part I of this series. IVS-PLS is based on a dimension-wise selective removal of single elements in the PLS weight vector w. IVS uses cross-validation (CV) as a guiding tool. The present paper illustrates the use of IVS-PLS on both simulated data and real examples from chemistry. In the first example, spectrophotometric data were simulated according to an experimental design. The objective was to see how IVS-PLS was influenced by different levels of noise in X and Y and by the number of predictor variables (K). The results of the modelling are shown as response surfaces. In addition, four real examples were modelled by the IVS-PLS technique. The real data sets were chosen to reflect different types of data from chemistry. For each example a comparison of ‘prediction error sum of squares’ (PRESS) between IVS-PLS and classical PLS is madeFor most of the examples containing many predictor variables IVS-PLS shows an improvement in predictive properties over classical PLS. Also, improvements for IVS-PLS2 (modelling of more than one y-variable) models were found. For data sets with a moderate number of variables the influence of the IVS method becomes less pronounced.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 8 (1994), S. 377-389 
    ISSN: 0886-9383
    Keywords: Kernel PLS regression ; Cross-validation ; Model dimensionality ; Multivariate image regression ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Multivariate images are very large data structures and any type of regression for their analysis is very computer-intensive. Kernel-based partial least squares (PLS) regression, presented in an earlier paper, makes the calculation phase more rapid and less demanding in computer memory. The present paper is a direct continuation of the first paper. In this study the kernel PLS algorithm is extended to include cross-validation for determination of the optimal model dimensionality. To show the applicability of the kernel algorithm, two examples from multivariate image analysis are used. The first example is an image from an airborne scanner of size 9 × 512 × 512. It consists of nine images which are regressed against a constructed dependent image to test the accuracy of the kernel algorithm when used on large data structures. The second example is a satellite image of size 7 × 512 × 512. Several different regression models are presented together with a comparison of their predictive capabilities. The regression models are also used as examples for showing the use of cross-validation.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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