Optimization of a response variable y constrained by principal directions of variations in the observation X-matrix
✍ Scribed by Ketil Svinning; Øystein Ingerøyen; Kjell Dalsveen
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 615 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0886-9383
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✦ Synopsis
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.