𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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

No coin nor oath required. For personal study only.

✦ 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.