MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: minimize avg distance to some points

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38315] Re: minimize avg distance to some points
  • From: Tom Burton <tburton at brahea.com>
  • Date: Thu, 12 Dec 2002 01:33:00 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

On 12/10/02 1:21 AM, in article at4blv$emc$1 at smc.vnet.net, "Daniel Reeves"
<dreeves at umich.edu> wrote:

> Given a list of n-dimensional points, find a point that minimizes the
> average distance to all the given points.
> 
> ...
> 
> Solve[eqs, {z[1], z[2], z[3]}]
> 
> But Mathematica chokes on that...
>
> Any ideas for a better algorithm to find the total-distance minimizing
> point (this should work for any dimensions; 16 in my case)?

Well, I happen to know the answer in three dimensions:

In[15]:=
centroid = Plus@@points/Length[points]
Out[15]=
 11  13  15
{--, --, --}
 2   2   2
In[16]:=
eqs /. Thread[Array[z,3]->centroid]
Out[16]=
{True, True, True}

Maybe you can extend this to n dimensions. I cannot do so, at least not
trivially. However, FindRoot worked nicely in the 16-dimensional examples I
tried.

Tom Burton



  • Prev by Date: Re: Why can't Mathematica find this root?
  • Next by Date: Re: Why can't Mathematica find this root?
  • Previous by thread: minimize avg distance to some points
  • Next by thread: Re: minimize avg distance to some points