Context

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Learned in this study

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Things to explore

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• Vocabulary
  • Size of vocabulary vs another entity
  • Overlapping/Intersecting vocabulary with another entity

Overview

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$$ Vocabulary\ of\ entity\ 1 = V_1 \\ Cardinality\ of\ the\ vocabulary\ of\ entity\ 1 = |V_1| $$$$ Vocabulary\ of\ entity\ 2 = V_2 \\ Cardinality\ of\ the\ vocabulary\ of\ entity\ 2 = |V_1| $$$$ Common\ vocabulary = V_1 \cap V_2 \\ Shared\ vocabulary = V_1 \cup V_2 \\ Vocabulary\ only\ in\ V_1 = V_1 - V_2 \\ Vocabulary\ only\ in\ V_2 = V_2 - V_1 \\ Uncommon\ vocabulary = (V_1 \cup V_2) - (V_1 \cap V_2) = (V_1 - V_2) \cup (V_2 - V_1) $$$$ Jaccard\ index = J(V_1, V_2) = \frac{|V_1 \cap V_2|}{|V_1 \cup V_2|} \\ Size\ relative\ Jaccard\ index = |V_1 \cap V_2| \times J(V_1, V_2) = 2 \frac{|V_1 \cap V_2|}{|V_1 \cup V_2|} $$$$ Overlap\ coefficient = overlap(V_1, V_2) = \frac{|V_1 \cap V_2|}{\min(|V_1|, |V_2|)} $$

See also

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References

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• https://en.wikipedia.org/wiki/Jaccard_index