I think the SVD-based method itself appears to be pretty interesting mainly due to its simplicity and because there is a straightforward linear algebra solution. However, I read the Pilu paper first and was amazed that he just describes the steps of the method and does not even try to explain why the method works (i.e. the pairing matrix P obtained is the orthogonal matrix that maximizes the inner product of P and G). He also doesn't even bother trying to explain the method in his own words, but cites full sentences from the original Scott & Longuet-Higgins paper.

OK. So much for complaining about the papers. I actually have a real question on what replacing the matrix D (which has singular values on the diagonal) with the matrix E (which has ones on the diagonal) in SVD will do in general? Especially if you think of SVD from the PCA viewpoint, you are amplifying the components with low singular values compared to those with high singular values. I'm not quite sure how to interpret this.