[EM] multidimensional medians

[Rob LeGrand]

Warren wrote:
> A notion of median friendly wth L2 distance is this:
> a point is a "2D median" if and only if,
> for every line thru that point which misses the others,
> exactly half the other points are
> on each side of it.

Perhaps a better generalization of median to higher dimensions is the
Fermat-Weber point, the point that minimizes the sum of the L2 distances
from it to each point.  (Average can be similarly generalized, minimizing
the sum of squared L2 distances.)  It always exists (of course) and is
unique unless you have an even number of collinear points and the middle
two are different.  It is also rotationally invariant.

--
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/


 
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