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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
    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
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  • 4
    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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