quasi
Posts:
12,062
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

