The Tversky index, named after Amos Tversky,[1] is an asymmetric similarity measure on sets that compares a variant to a prototype.
The Tversky index can be seen as a generalization of the Sørensen–Dice coefficient and the Jaccard index.
For sets X and Y the Tversky index is a number between 0 and 1 given by
+ β
denotes the relative complement of Y in X.
α , β ≥ 0
are parameters of the Tversky index.
α = β = 1
produces the Jaccard index; setting
α = β = 0.5
produces the Sørensen–Dice coefficient.
If we consider X to be the prototype and Y to be the variant, then
corresponds to the weight of the prototype and
β
corresponds to the weight of the variant.
Tversky measures with
α + β = 1
are of special interest.
[2] Because of the inherent asymmetry, the Tversky index does not meet the criteria for a similarity metric.
However, if symmetry is needed a variant of the original formulation has been proposed using max and min functions[3] .
+ β
, This formulation also re-arranges parameters
controls the balance between
controls the effect of the symmetric difference