Table 1 Mathematical expressions for several similarity and dissimilarity measures
Metric name | Notation | Expression |
|---|---|---|
Jaccard similarity | J(A, B) | \(\frac{|A \cap B|}{|A \cup B|}\) |
Containment index | C(A, B) | \(\frac{|A \cap B|}{|A|}\) |
Cosine similarity (also known as Otsuka-Ochiai) | \(\cos \theta\) | \(\frac{|A \cap B|}{\sqrt{|A|\cdot |B|}}\) |
Kulczynski 1 | \(K_1(A,B)\) | \(\frac{|A \cap B|}{|A \Delta B|}\) |
Kulczynski 2 | \(K_2(A,B)\) | \(\frac{1}{2} \Big ( \frac{|A \cap B|}{|A|} + \frac{|A \cap B|}{|B|} \Big )\) |
Whittaker distance | W(A, B) | \(1 - \frac{1}{2} \Big ( \frac{|A \cap B|}{|A|} + \frac{|A \cap B|}{|B|} \Big )\) |
Sorensen index | S(A, B) | \(2 \frac{|A \cap B|}{|A| + |B|}\) |
Bray-Curtis dissimilarity | BC(A, B) | \(1 - 2 \frac{|A \cap B|}{|A| + |B|}\) |