which is the distance between the original point on this projection on a principal subspace and so the the grayscale here represent that energy okay zero energy on the principal subspace and energy that goes quadratic quadratically as you move away obviously this is not a good representation of that data manifold this is the data okay so the data points are sampled from this spiral and PCA doesn't do a good job at this right k-means has a funny kind of energy function which is not directly doesn't have a sort of direct form but