Does the magnitudes of principal eigenvectors obtained by PCA have anything to do with correlations of original variables, and can we use PCA for clustering? Thanks!
@ q2: Ifyou use all principal components, then this is only a rotation in the multidimensional space and the euclidean(!) distances between datapoints are not affected.
However, for instance taxicab-distances are affected by rotation. (This ca be seen if you consider the unit square and the taxicab-distance between the two edges of the diagonal. Unrotated you have two times one border s the distance is 2, but if you rotate it by 45 deg you have the distance sqrt(2))
Furthermore, once you employ PCA then your goal is to reduce dimensionality, thus usually you discard variance/covariance (according to the ignored less-principal components), and this cannot be reflected by any selection of sets of items in a "canned" cluster-analysis, so the solutions must be different.