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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: 12,067 Registered: 7/15/05
Re: Question: Centroid given a distance metric
Posted: Feb 12, 2013 3:24 AM

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

Date Subject Author
2/11/13 quasi
2/12/13 quasi
2/12/13 quasi
2/12/13 quasi
2/11/13 David Bernier
2/12/13 quasi
2/12/13 quasi
2/11/13 quasi
2/12/13 Ray Koopman