Tversky index

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S(X, Y) = \frac{| X \cap Y |}{| X \cap Y | + \alpha | X - Y | + \beta | Y - X |} ,

Here, X - Y denotes the relative complement of Y in X.

Further, \alpha, \beta \ge 0 are parameters of the Tversky index. Setting \alpha = \beta = 1 produces the Tanimoto coefficient; setting \alpha = \beta = 0.5 produces Dice's coefficient.

If we consider X to be the prototype and Y to be the variant, then \alpha corresponds to the weight of the prototype and \beta corresponds to the weight of the variant. Tversky measures with \alpha + \beta = 1 are of special interest.[2]


S(X,Y)=\frac{| X \cap Y |}{| X \cap Y |+\beta\left(\alpha a+(1-\alpha)b\right)},

a=\min\left(|X-Y|,|Y-X|\right) ,

b=\max\left(|X-Y|,|Y-X|\right) ,

This formulation also re-arranges parameters \alpha and \beta . Thus,  \alpha controls the balance between  |X - Y| and  |Y - X| in the denominator. Similarly, \beta controls the effect of the symmetric difference  |X\,\triangle\,Y\,| versus  | X \cap Y | in the denominator.


  2. ^