Considering how much I learned from Davis’ little example, I almost hate to summarize it. The following just does not do justice to it. We’ll see if the passage of time – coming back to Davis with fresh eyes after doing the next example – improves the summary.
OTOH, an awful lot of what I got out of Davis came from bringing linear algebra to it, and just plain mucking about with the matrices. And I discovered, having picked up the two chemistry books since I drafted this post, that they made a lot more sense than when I first looked at them. I have learned a lot from working with Davis’ example.
Here’s what I have. My own strong preference, but I’d call it a personal choice, is to use the SVD of the data matrix X:
and compute the A’s and S’s (R-mode and Q-mode loadings and scores):
Those equations are worth having as a conceptual basis even if one chooses to do eigendecompositions of or instead of the SVD.
Read the rest of this entry »