that is perfectly reconstructed is the principal subspace right in this case here if the data points are sampled from this from the sparrow the principal subspace here dimension 1 is this so this has become our reconstruction error 0 and everything else grows could racket quadratically right because you take a point you project it on this and so if it's already there reconstruction here at zero if it's here reconstruction error scores that the square of the Euclidean distance not a good model of a spiral as you can tell k-means says so