Hi,
I have working on an optimisation problem and have performed some PCA on the dataset. The top seven principal components explain about 80% of the variance. I was hoping to plan a DoE using these top seven principal components as variables. However, a colleague has indicated that this is rubbish as the later principal components explain comparatively little variance versus the earlier ones and as such their inclusion would lead to an inefficient use of experimental resource. (For info, he instead advocated for k nearest neighbour analysis, which I don't know much about). My query is whether it is still valid to do a DoE with variables (in this case principal components) that vary widely in their ability to explain data. (In my area, I often see DoEs proposed based on just the top three DoEs, even when they only explain a fraction of the overall variability.)
