quasi
Posts:
9,078
Registered:
7/15/05
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Re: Question: Centroid given a distance metric
Posted:
Feb 12, 2013 3:24 AM
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Andrey Savov wrote:
>quasi wrote:
>>
>> Can you give a concrete example, specifying
>> n
>> a norm on R^n
>> a finite set of points in R^n
>
>http://en.wikipedia.org/wiki/Centroid#Of_a_finite_set_of_points
No, you misunderstood.
It's easy to find the centroid of a finite set of points in R^n
where R^n where centroid is defined in the usual way.
You were asking about how, for a norm on R^n other than the
standard one, and for a given finite set of points in R^n, to
find a point in R^n which minimizes the sum of the squares of
the distances to the points of that set, and where distances
are with respect to the given norm.
I was asking for a _numerical_ example with an actual value
of n, an actual norm on R^n other than the the Euclidean norm,
and an actual finite set of points for which the goal is
to find a point which minimizes the sum of the squares of
the distances to the given set. In other words, a concrete
example of a mimimization problem of the type you are
interested in.
quasi
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