publication . Other literature type . Article . 1987

Multi-way principal components-and PLS-analysis†

Svante Wold; Paul Geladi; Kim Esbensen; Jerker Öhman;
  • Published: 01 Jan 1987
  • Publisher: Wiley
Abstract
The Lohmoller–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 unfoldi...
Subjects
free text keywords: Analytical Chemistry, Applied Mathematics, Latent variable, Non-linear iterative partial least squares, Pattern recognition, Statistics, Score vector, Matrix (mathematics), Partial least squares regression, Principal component analysis, Artificial intelligence, business.industry, business, Mathematics, Least squares, Econometrics, Eigenvalues and eigenvectors
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