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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:

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

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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
up vote 3 down vote accepted

This seems related to cluster analysis, and your d(A, B) is used in "average linkage clustering."

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