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I wanted to exactly understand how Partial Least Squares Regression works and thus got my hands onto a paper called "A Simple Explanation of Partial Least Squares". After some thinking and consulting on other related papers and tutorials I think I found something strange in what is presented to be the PLS-NIPALS algorithm here Link to paper.

Algorithm description from the paper

From my understanding what is denoted as P here are the weights that are usually denoted as W. But then, X is deflated with what appears to be the weights when it should be deflated using the loadings. (I've never see the loadings corresponding to X be calculated anywhere in this presentation of the algorithm)

Is this normal? Is it a mistake from the creator?

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