title: How to calculate distance from center of a hypersphere (whitened PCA)
body: <p>Lets say that I have calculated the principal components of a reference data set including whitening. The transformation matrix created from the principal component vectors is then applies to a test data set, projecting it onto the subspace of PCs. Now, I should be able to measure the distance of each of the test data vectors from the center of the PC hypersphere by simply adding up the coefficients of each column. Is this correct? Applying this transformation to my reference data gives a length of zero for all columns, and the length of the vectors seems to decrease as I make the test data look more like the reference data and grows as I make the two sets more distinct. </p>
  
  <p>Am I correct that I can judge "distance" in a multidimensional space in this way? Is it just the sum of the coefficients of the projected matrix? </p>
  
  <p>Thanks very much for any insight you can provide. </p>