There's not much software here in this presentation, but the most common ones used in chemometrics would be Unscrambler, Simca and PLS_Toolbox. But there are many other nice packages as well
+Novatures I guess it is because P is an orthogonal matrix, i.e., P*P'=P'*P=I. And this is an constrain condition when we optimizing P (the projection matrix).
If you check out the gray line in gray font at the upper right corner of the slide 9:00, it says there's a simplification for weights (also rotations) and loadings. For simplicity, the tutorial use the same symbol P to denote both the loading and rotation. In reality (for example in scikit-learn.org/stable/modules/generated/sklearn.cross_decomposition.PLSRegression.html), it should be T = XP' + E and T = X W(P'W)^{-1}, in which W denotes the weights for X. The difference between a loading and a weighting is documented at wiki.eigenvector.com/index.php?title=Faq_difference_between_a_loading_and_a_weighting. I would agree with the tutorial on simplifying those symbols when introducing PLSR at the first time (especially following PCA), which makes it easier to understand PLSR easier at a high level.
Thank for this! Helped a lot with the understanding of making prediction using the regression (B) matrix.
which software this is?
There's not much software here in this presentation, but the most common ones used in chemometrics would be Unscrambler, Simca and PLS_Toolbox. But there are many other nice packages as well
what does R matrix stands for ?
That's the matrix containing the inner relation regression coefficients on the diagonal
I don't understand why T=X*P, since X = T*P'+E :(
+Novatures I guess it is because P is an orthogonal matrix, i.e., P*P'=P'*P=I. And this is an constrain condition when we optimizing P (the projection matrix).
If you check out the gray line in gray font at the upper right corner of the slide 9:00, it says there's a simplification for weights (also rotations) and loadings. For simplicity, the tutorial use the same symbol P to denote both the loading and rotation. In reality (for example in scikit-learn.org/stable/modules/generated/sklearn.cross_decomposition.PLSRegression.html), it should be T = XP' + E and T = X W(P'W)^{-1}, in which W denotes the weights for X. The difference between a loading and a weighting is documented at wiki.eigenvector.com/index.php?title=Faq_difference_between_a_loading_and_a_weighting. I would agree with the tutorial on simplifying those symbols when introducing PLSR at the first time (especially following PCA), which makes it easier to understand PLSR easier at a high level.