Tversky index

$$sim_{Tversky}(x, y) = \frac{|x \cap y|}{|x \cap y| + \alpha |x \setminus y| + \beta |y \setminus x|}$$

Where:

• $x \setminus y$ denotes the relative complement of $y$ in $x$.
• $\alpha, \beta \ge 0$ are parameters of the Tversky index.
  • $\alpha = \beta = 1$ produces the Jaccard index
  • $\alpha = \beta = \frac{1}{2}$ produces the Dice coefficient

The Tversky index can be seen as a generalization of the Dice coefficient and the Jaccard index.

Reading

• Tversky, Amos. “Features of Similarity.” Psychological Review 84 (1977): 327-352.