PCA can be considered an affine transformation: When we consider a 2D dataset and compute its projection onto the 2 principal axes, we come up with another 2D dataset - the principal components. These are just points which are rotated and maybe scaled with respect to the original dataset.
Now, my question: How do we find out the affine transformation / rotation matrix that converts the original dataset to the principal components?
I know how the SVD can be used to perform PCA. Basically, after we perform SVD on the original data, we end up with:
Data = U * Sigma * V^T PCs = U * Sigma = Data * V eigenVals = Sigma**2 / (self.m - 1), where there are m rows in Data eigenVecs = V
So, I get the PCs simply by multiplying the data-matrix with V. But this does not make V my affine transform, does it? Sorry to be so confused.