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just a quick question. Suppose I have two sets $A,\,B$. Is there a specific name for the following similarity measure?

$$\operatorname{sim}(A,B) = \frac{|A \cap B|}{\max\{|A|,|B|\}}$$

It is slightly different from the Jaccard coefficient, but I can't find the proper name for this formula.

J.G.
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Mikołaj Morzy
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  • This can probably benefit from additional tags. The set theory ones, however, are not amongst them. – Asaf Karagila May 21 '15 at 10:14
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    You should enforce $A$ and $B$ to be finite nonempty sets, else the formula is bogus. – AlexR May 21 '15 at 10:26
  • Interesting. Just out of curiosity, what is your motivation for considering that particular formula, as opposed to $|A \cap B|/\mbox{[something else]}$? – goblin GONE May 21 '15 at 10:35
  • This is just a small part inside an algorithm that searches through a large volume of data for frequent patterns. In reality A and B are collections of sets induced by individual items (i.e. A is a collection of all frequent itemsets which form a frequent itemset with an item a, and B is a collection of all frequent itemsets which form a frequent itemset with an item b). – Mikołaj Morzy May 22 '15 at 10:52
  • I am trying to find to what extent items a and b appear in the same context in the database of transactions, and the context will be more similar, if the overlap between these collections of frequent itemsets were relatively large. Anyway, I'm just interested if someone knows the name of this formula. – Mikołaj Morzy May 22 '15 at 10:52

1 Answers1

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This similarity meaure $\frac{|A\cap B|}{\max(|A|,|B|)}$ is called Braun-Blanquet similarity, while the variant $\frac{|A\cap B|}{\min(|A|,|B|)}$ is called Simpson Similarity, Overlap Similarity, Overlap Coefficient or Szymkiewicz–Simpson coefficient.

Sources:

  1. Encyclopedia of Distances by Deza and Deza: https://link.springer.com/book/10.1007/978-3-642-30958-8
  2. https://en.wikipedia.org/wiki/Overlap_coefficient
J.G.
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Nikos Gialitsis
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