In the SIMPLS formulation of partial least squares (PLS) regression, the weights are constrained to have length of 1,
$$r_a^Tr_a = 1,$$ where $a$ represents a latent component (from $1$ to $A$). This is from the original definition by de Jong (1993).
plsgenomics package says in the help for the
In the original definition of SIMPLS by de Jong (1993), the weight vectors have length 1. If the weight vectors are standardized to have length 1, they satisfy a simple optimality criterion (de Jong, 1993).
I read de Jong's paper and he says:
For the development of the theory and algorithm of SIMPLS it was convenient to choose normalized weight vectors $r_a$. This choice, however, is in no way essential.
My question is this. Can anyone give me an intuition for what effect constraining the length of the weight vector has on the algorithm?
- de Jong, S. SIMPLS: an Alternative Approach To Partial Least-Squares Regression. Chemom. Intell. Lab. Syst. 18, 251–263 (1993).