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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