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?