Analysis of projection Utilizes Pythagoras' theorem Assumes distance function is a metric distance Works fine for the first coordinate in the reduced dimensionality Need a way to extend and generalize this Assume an original dimensionality of After first step project everything onto a -hyperdimensional plane which is perpendicular to line Modify distance to work for dimensions Modified distance may not be a metric distance any more Will be a metric if in Euclidean space Coordinates may be negative   Possible but unlikely since and should have been pivots