quasi
Posts:
9,095
Registered:
7/15/05
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Re: Question: Centroid given a distance metric
Posted:
Feb 12, 2013 4:03 AM
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Andrey Savov wrote:
>
>> On Monday, February 11, 2013 11:45:19 PM UTC-8, quasi wrote:
>> > Can you give a concrete example, specifying
>> > n
>> > a norm on R^n
>> > a finite set of points in R^n
>
>Also
>
>http://en.wikipedia.org/wiki/Norm_(mathematics)#Euclidean_norm
>http://en.wikipedia.org/wiki/Euclidean_distance#N_dimensions
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>So the centroid point as defined by
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>http://en.wikipedia.org/wiki/Centroid#Of_a_finite_set_of_points
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>minimizes the Euclidean distance between itself and each point in
>the set.
No, it minimizes the sum of the squares of the distances.
But in any case, for the Euclidean norm on R^n, finding the
centroid of a finite set of point is trivial.
Your question was to find an analogous point with respect to
a metric other than the Euclidean metric.
Of course, in the non-Euclidean case, the sum of the squares
of the distances is probably not a geometrically interesting
thing to minimize.
quasi
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