In projectionbased clustering. we note that, if the data is well separated into clusters with means #1, . . . ,pK. then the top H eigenvectors of the data covariance matriJ-c1 say {1:1, . . . ,tIK), tend to align with the Spanu, . . . ,pg}. It follows that PEA will approximately preserve the distance between cluster means. This intuition (and choice of projection} implicitly assum that the Euclidean metric is the right way of measuring distance for our particular data. Where is that assumption coming in? 1ll'll'hat would you do otherwise. i.e.. if it turns out that a different notion of distance dist{Xi,Xj] were more appropriate. would you prefer some other transformation over PEA