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Optimization of a response variable y constrained by principal directions of variations in the observation X‐matrix
Author(s) -
Svinning Ketil,
Ingerøyen Øystein,
Dalsveen Kjell
Publication year - 2000
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/1099-128x(200009/12)14:5/6<699::aid-cem643>3.0.co;2-k
Subject(s) - principal component analysis , mathematical optimization , optimization problem , matrix (chemical analysis) , component (thermodynamics) , mathematics , constraint (computer aided design) , principal component regression , function (biology) , partial least squares regression , constrained optimization , algorithm , statistics , materials science , physics , geometry , evolutionary biology , biology , composite material , thermodynamics
A method for optimization constrained by principal directions of variations in an observation X ‐matrix is developed. The optimization has the form of a linear program/linear programs, where the constraints describing the influence of one variable on the others are given by one PLS component or a combination of several. In the case of more than one PLS component included in the optimization, a stepwise optimization is performed, making a new PLS component constraint with new loadings before each optimization. A solution of the optimization is achieved by letting the new loadings be equal to linear combinations of the original ones, and a search for the linear combination giving the optimal point is performed. As an example, an optimization of the compressive strength of cement as a function of the particle size distribution is shown. The function is a result of partial least squares regression (PLS) on 120 observations. Copyright © 2000 John Wiley & Sons, Ltd.