I'm trying to understand the equation for partial least squares (PLS) regression from the paper "A survey of partial least squares (PLS) methods, with emphasis on the two-blocks case". I'm having trouble understanding how the equation is derived based on the paper. Can someone please explain it to me? Here is a more detailed explanation of the question:
The equation for PLS regression is given in the paper as follows:
$$ \hat{X}_1(\epsilon_1) = \epsilon_1((\epsilon_1^T \epsilon_1)^{-1} \epsilon_1^T X_1) $$
This paper tell me that we want to regress