How the distance between sets is called? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T23:42:13Z http://mathoverflow.net/feeds/question/58301 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58301/how-the-distance-between-sets-is-called How the distance between sets is called? Dair T'arg 2011-03-13T01:04:17Z 2011-03-13T04:27:41Z <p>Hello,</p> <p>I've recently write down some measure for sets and now I wonder how it is called or where it is described?</p> <p>The measure itself is the following: Let $A$ &amp; $B$ -- two sets of values from a single space (real line for example) Let:</p> <p>$d(A, B) = \sum_{a \in A} \sum_{b \in B} \frac{dist(a, b)}{len(A) * len(B)}$</p> <ul> <li>$dist(a, b)$ is the distance between two values</li> <li>$len(A)$ is the number of the elements in $A$</li> </ul> <p>So, the measure itself is:</p> <p>$|| A, B || = \frac{d^2(A, B)}{|d(A, A) d(B, B)|} - 1$</p> http://mathoverflow.net/questions/58301/how-the-distance-between-sets-is-called/58309#58309 Answer by noppoli for How the distance between sets is called? noppoli 2011-03-13T02:46:06Z 2011-03-13T02:46:06Z <p>This seems related to cluster analysis, and your d(A, B) is used in "average linkage clustering." <a href="http://en.wikipedia.org/wiki/Cluster_analysis" rel="nofollow">http://en.wikipedia.org/wiki/Cluster_analysis</a></p>