I think Ted is suggesting augmenting the vectors to (1,0,0,100) and (10,0,0,100) and projecting onto the unit sphere in 4 dimensions. Then the distance is not 0 on the surface of that sphere.
On Fri, Jul 22, 2011 at 7:29 AM, Jake Mannix <[email protected]> wrote: > (1, 0, 0) and (10, 0, 0) have very large distance in R^3, but 0 when > projected onto > the a patch near the north pole of S^4, while other pairs of vectors may > have > (nearly) unchanged distances. > > Am I misunderstanding what the question was? > > On Thu, Jul 21, 2011 at 9:43 PM, Ted Dunning <[email protected]> > wrote: > > > Embed onto a very small part of S^4 > > > > On Thu, Jul 21, 2011 at 9:14 PM, Jake Mannix <[email protected]> > > wrote: > > > > > Think about it in 3-dimensions, how can this work? > > > > > >
