ISSN:
0886-9383
Keywords:
PLS regression
;
orthogonal expansion
;
optimization
;
Lagrange multipliers
;
Chemistry
;
Analytical Chemistry and Spectroscopy
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
A simple iteration algorithm that is faster and less memory-intensive than the NIPALS iteration algorithm for PLS regression is presented. The iteration algorithm is obtained by treating the orthogonal expansion or decomposition of a matrix X as an extremum problem subject to normalization and orthogonality constraint conditions and then solving the problem by use of the method of Lagrange multipliers. The main idea in this method is to find the transformation vector r. The latent variable t is expressed exactly as the linear combination of X-variables with the vector r so that the final regression coefficients can be conveniently provided. In the algorithm the recursion of the orthogonal projection is needed, which is derived by use of a matrix inverse formula. Algorithms are established from the equation for calculating the vector r that are suitable for dealing with three cases of large data sets. The first case is when the number of objects is very large, the number of variables is relatively small and the number of Y-variables is equal to or greater than the number of X-variables. The second case is when the number of objects is very large, the number of variables is relatively small and the number of X-variables is greater than the number of Y-variables. The last case is when the number of variables, either X- or Y-variables, or both, is very large and the number of objects is small.
Additional Material:
4 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/cem.1180090504
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