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Topic: Question: Centroid given a distance metric
Replies: 14   Last Post: Feb 12, 2013 1:04 PM

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quasi

Posts: 10,188
Registered: 7/15/05
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
>
>So the centroid point as defined by
>
>http://en.wikipedia.org/wiki/Centroid#Of_a_finite_set_of_points
>
>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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