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From Sean Owen <sro...@gmail.com>
Subject Re: Preserving pairwise distances while normalizing vectors
Date Fri, 22 Jul 2011 07:46:28 GMT
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 <jake.mannix@gmail.com> 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 <ted.dunning@gmail.com>
> wrote:
>
> > Embed onto a very small part of S^4
> >
> > On Thu, Jul 21, 2011 at 9:14 PM, Jake Mannix <jake.mannix@gmail.com>
> > wrote:
> >
> > > Think about it in 3-dimensions, how can this work?
> > >
> >
>

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