quasi
Posts:
12,012
Registered:
7/15/05


Re: Question: Centroid given a distance metric
Posted:
Feb 12, 2013 4:03 AM


Andrey Savov wrote: > >> On Monday, February 11, 2013 11:45:19 PM UTC8, 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 nonEuclidean case, the sum of the squares of the distances is probably not a geometrically interesting thing to minimize.
quasi

