Global InformationTversky index information
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
Here, denotes the relative complement of Y in X.
Further, are parameters of the Tversky index. Setting produces the Jaccard index; setting 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 corresponds to the weight of the variant. Tversky measures with 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] .
,
,
This formulation also re-arranges parameters and . Thus, controls the balance between and in the denominator. Similarly, controls the effect of the symmetric difference versus in the denominator.
- ^ Tversky, Amos (1977). "Features of Similarity" (PDF). Psychological Review. 84 (4): 327–352. doi:10.1037/0033-295x.84.4.327.
- ^ "Daylight Theory: Fingerprints".
- ^ Jimenez, S., Becerra, C., Gelbukh, A. SOFTCARDINALITY-CORE: Improving Text Overlap with Distributional Measures for Semantic Textual Similarity. Second Joint Conference on Lexical and Computational Semantics (*SEM), Volume 1: Proceedings of the Main Conference and the Shared Task: Semantic Textual Similarity, p.194-201, June 7–8, 2013, Atlanta, Georgia, USA.