Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Hello,

I've recently write down some measure for sets and now I wonder how it is called or where it is described?

The measure itself is the following: Let $A$ & $B$ -- two sets of values from a single space (real line for example) Let:

$d(A, B) = \sum_{a \in A} \sum_{b \in B} \frac{dist(a, b)}{len(A) * len(B)}$

  • $dist(a, b)$ is the distance between two values
  • $len(A)$ is the number of the elements in $A$

So, the measure itself is:

$|| A, B || = \frac{d^2(A, B)}{|d(A, A) d(B, B)|} - 1$

share|improve this question
    
By the way, "measure-theory" refers to something specific which is not the same as what you are talking about. I've taken the liberty of changing the tags –  Yemon Choi Mar 13 '11 at 4:26
    
a minor point: the notation is somewhat unfortunate, because normally one would expect $d(A,A)$ to be zero (notationally speaking). –  Suvrit Mar 13 '11 at 12:34
add comment

1 Answer

up vote 3 down vote accepted

This seems related to cluster analysis, and your d(A, B) is used in "average linkage clustering." http://en.wikipedia.org/wiki/Cluster_analysis

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.