Compute the Tversky index

Computes the Tversky index between two sets, a generalisation of the Jaccard and Sørensen–Dice similarity coefficients. The index measures the overlap between x and y relative to their differences, weighted by alpha and beta.

The Tversky index is defined as:

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

Special cases:

• alpha = beta = 0.5 — Sørensen–Dice coefficient

• alpha = beta = 1.0 — Jaccard index

Usage

compute_tversky_index(x, y, alpha = 0.5, beta = 0.5)

Arguments

x

A vector. Coerced to character before comparison.

y

A vector. Coerced to character before comparison.

alpha

Non-negative numeric. Weight applied to elements in x but not in y. Defaults to 0.5.

beta

Non-negative numeric. Weight applied to elements in y but not in x. Defaults to 0.5.

Value

A single numeric value in the range [0, 1], where 0 indicates no overlap and 1 indicates identical sets.

Note

Both x and y are treated as sets — duplicate elements within each vector are ignored. Inputs are coerced to character before comparison, so 1L and "1" are treated as equal.

Examples

x <- c("a", "b", "c", "d")
y <- c("b", "c", "d", "e")

# default (Sorensen-Dice)
compute_tversky_index(x, y)
#> [1] 0.75

# Jaccard index
compute_tversky_index(x, y, alpha = 1, beta = 1)
#> [1] 0.6

# asymmetric: penalise x-only elements more heavily
compute_tversky_index(x, y, alpha = 0.9, beta = 0.1)
#> [1] 0.75

# identical sets → 1
compute_tversky_index(x, x)
#> [1] 1

# disjoint sets → 0
compute_tversky_index(c("a", "b"), c("c", "d"))
#> [1] 0