Date: Feb 13, 2013 7:25 AM
Author: quasi
Subject: Re: Question: Centroid given a distance metric
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 p-norm 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 over-generalized 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