Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.


quasi
Posts:
9,925
Registered:
7/15/05


Re: Question: Centroid given a distance metric
Posted:
Feb 13, 2013 7:25 AM


Andrey Savov wrote: >Ray Vickson wrote: >> >>I would ask: why do you want to minimize the sum of squares? >>For Euclidean distance, that F(x) has some physical and >>statistical meaning, and furthermore leads to a simple >>solution. However, for other norms such as d(x,y) = x+y >>or d(x,y) = max(x,y), or for a pnorm with 1 < p < 2, >>what significance can one attach to the sum of squares? >>Certainly it makes _some_ problems much harder instead of >>easier (for example, when d(x,y) = x + y). > >The norms I had in mind were actually much nicer than the >ones you mention.
Actually, _you_ were the one who mentioned the taxicab norm when I asked for a concrete example of a norm other than the standard Euclidean one to be used as a test case to discuss the questions you raised.
>They were continuous and even convex functions on a subset >of R^n, so for them that point has meaning similar to the >Euclidean norm.
Let's see an example.
>I overgeneralized when I posted the question.
Yep.
So why not try to fix it?
Clarify your assumptions and state what you think is true based on those assumptions.
quaai



