I want to compare solutions provided by two instances of PCA, either due to two different implementations or due to two subsets of the data.
One possible way is to calculate the similarity between the loadings (e.g. using the inner product). But as this post discusses, the signs of the loadings elements are meaningless.
Then, what is the correct way to compare the two PCA outputs?
Is it valid to just take the absolute of the loadings?
There is some confusion about loadings and eigenvectors. I am using loadings to say the eigenvetors scaled up by the square root of corresponding eigenvalues. So, which one is (loadings or eigenvectors) the better choice to compare the PCA solutions and why?
PS: @ttnphns commented that using loadings is the right thing to do but it is not clear to me why.