- The score matrix contains the projections of your original data onto the principal components. Each row corresponds to an observation, and each column corresponds to a principal component.
- The rotatefactors function computes a rotation matrix (TransfMatrix) that rotates the original principal component axes to achieve a simpler or more interpretable structure (e.g., varimax rotation).
- Finally, the multiplication score * TransfMatrix applies this rotation to the scores. This operation effectively re-projects the original data onto the new rotated axes, resulting in NewScores. In matrix multiplication terms, this means each row of score (representing an observation) is transformed by the columns of TransfMatrix (representing the rotated axes).
Apply 'rotatefactors' on the observations to represent them in the new factorial design (PCA)
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Hi all,
I guess, that it is an easy issue, but I can not figure out how to apply rotatefactors on the SCORES matrix resulting from a previous PCA:
(1) I run a PCA following:
[wcoeff,score] = pca(zscore(DataSet))
(2) I would like to rotate my principal components using rotatefactors:
[NewCoeff,TransfMatrix] = rotatefactors(wcoeff);
NewCoeff should give the new coordinates of the variables on the varimax-rotated components.
My question is: How can I compute the coordinates 'NewScores' of my observations on the new components? My idea is to plot them on a biplot and on an other scatter-plot where each axis is a component. I guess that there is something easy like:
NewScores = score * TransfMatrix
Am I right?
Romain
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Answers (1)
Ayush Aniket
on 22 Jan 2025 at 4:01
Yes, your approach to compute the new scores after applying a rotation to the principal components is correct. When you apply rotatefactors to the loading matrix (wcoeff), you get a transformation matrix (TransfMatrix) that you can use to transform the original scores (score) to the new rotated component scores (NewScores). Here's a breakdown of why this is the correct approach:
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