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  • 1
    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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  • 2
    Electronic Resource
    Electronic Resource
    Notes on the history and nature of partial least squares (PLS) modelling (1988)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 2 (1988), S. 231-246 
    Details
    ISSN: 0886-9383
    Keywords: Partial least squares models ; History of PLS ; Soft versus hard modelling ; Latent variables ; Path models ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The growing awareness of the need for non-deterministic and distribution-free (soft) models combined with an iterative algorithm for finding latent variables led to the construction of partial least squares models. There have been separate developments in the humanistic and the natural sciences, with stress on different aspects and a different terminology. The historical development is described and some key topics are explained.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180020403
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Source contributions to ambient aerosol calculated by discriminat partial least squares regression (PLS) (1988)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 2 (1988), S. 281-296 
    Details
    ISSN: 0886-9383
    Keywords: Partial least squares ; Receptor modelling ; Colinearities ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Partial least squares regression (PLS) is proposed for solving ir pollution source apportionment problems as an alternative method to the frequently used chemical mass balance technique. A discriminant PLS is used to calculate linear mixing proportions for a synthetic ambient aerosol data set where the truth is known. Without sacrificing orthogonality of the source profiles, PLS can resolve the emission sources and accurately predict the emission source contributions. Further extensions of the PLS approach to environmental receptor modelling are discussed.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180020406
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Relationships between higher-order data array configurations and problem formulations in multivariate data analysis (1989)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 3 (1989), S. 33-48 
    Details
    ISSN: 0886-9383
    Keywords: Higher-order data arrays ; Dimensionality ; Data modelling ; Classification ; Discrimination ; Correlation ; Regression ; Systematics of data analysis ; Opportunities for future developments ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A scaffold for detailed understanding of the concept ‘dimensionality’ in data analysis is furnished by a systematic classification of higher-order data array configurations. Three major types of problem formulation in multivariate data analysis can be characterized for relevant data classes: 1data description (intra-class data structure modelling of inter-object and inter-variable relationships)2classification (inter-class discrimination)3correlation, regression (inter-variable relationships).The relationship between these three categories of data analytical problem formulation and the fundamental data array classification is exposed. These relations are augmented to include the general case of data arrays of order R, and R-way data analysis with the use of bilinear projections is presented. Based upon this, some possible directions for the future development of data analysis may be imagined.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180030106
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Can image analysis provide information useful in chemistry? (1989)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 3 (1989), S. 419-429 
    Details
    ISSN: 0886-9383
    Keywords: Image analysis ; Chemical imaging ; Multivariate image analysis ; Image analysis for non-imaging techniques ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Images can contain chemical information and many chemical methods can generate image data. For an efficient extraction of chemical data from images, data analysis techniques are necessary. It is a great advantage to be able to work on multivariate images. Many imaging techniques allow the extraction of chemical information. Inorganic analytical chemistry seems to have the longest tradition here, but organic chemistry and biochemistry may soon be catching up. Also large data arrays from non-imaging techniques can be combined with image analysis in a useful way, provided certain conditions are fulfilled.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180030209
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    Paper (German National Licenses)
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