Saturday, July 12, 2014

Sørensen-Dice coefficient - Wikipedia, the free encyclopedia

Sørensen's original formula was intended to be applied to presence/absence data, and is

QS = \frac{2C}{A + B} = \frac{2 |A \cap B|}{|A| + |B|}

where A and B are the number of species in samples A and B, respectively, and C is the number of species shared by the two samples; QS is the quotient of similarity and ranges from 0 to 1.[5] which is always in [0, 1] range.

It can be viewed as a similarity measure over sets:

s = \frac{2 | X \cap Y |}{| X | + | Y |}

Similarly to Jaccard, the set operations can be expressed in terms of vector operations over binary vectors A and B:

s_v = \frac{2 | A \cdot B |}{| A |^2 + | B |^2}

which gives the same outcome over binary vectors and also gives a more general similarity metric over vectors in general terms.


Read full article from Sørensen–Dice coefficient - Wikipedia, the free encyclopedia

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