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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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Posts: 12,067
Registered: 7/15/05
Re: Question: Centroid given a distance metric
Posted: Feb 11, 2013 12:50 PM
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Andrey Savov wrote:
>Andrey Savov wrote:
>> Was wondering if you guys can point me in the right direction.
>> Are there any known/studied methods to calculate a centroid
>>(geometric center) of finite set of points in n-dimensional
>>real Euclidean space by only knowing a distance metric
>>f(x,y): R^n x R^n -> R ?

>Should have been a bit more clear. I am looking to find the
>point in R^ that minimizes the square of the given metric
>between itself and the given points. For Euclidean distance
>metric that point would be sum(x_i)/k.

Is the metric derived from a norm?

For a general metric on R^2, what is the significance of the
sum of the squares of the distances to a given point? And what
jusifies calling a point which minimizes that sum for a given
finite set of points "the centroid" of that set?


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