Jaccard Similarity Index

Measure to compare two or more sets w.r.t. their similarity.

Usage

jaccard(sets, na_value = NaN, ...)

Arguments

sets: (list())
List of character or integer vectors. sets must have at least 2 elements.
na_value: (numeric(1))
Value that should be returned if the measure is not defined for the input (as described in the note). Default is NaN.
...: (any)
Additional arguments. Currently ignored.

Value

Performance value as numeric(1).

Details

For two sets $A$ and $B$, the Jaccard Index is defined as $$ J(A, B) = \frac{|A \cap B|}{|A \cup B|}. $$ If more than two sets are provided, the mean of all pairwise scores is calculated.

This measure is undefined if two or more sets are empty.

Meta Information

Type: "similarity"
Range: $[0, 1]$
Minimize: FALSE

References

Jaccard, Paul (1901). “Étude comparative de la distribution florale dans une portion des Alpes et du Jura.” Bulletin de la Société Vaudoise des Sciences Naturelles, 37, 547-579. doi:10.5169/SEALS-266450 .

Bommert A, Rahnenführer J, Lang M (2017). “A Multicriteria Approach to Find Predictive and Sparse Models with Stable Feature Selection for High-Dimensional Data.” Computational and Mathematical Methods in Medicine, 2017, 1–18. doi:10.1155/2017/7907163 .

Bommert A, Lang M (2021). “stabm: Stability Measures for Feature Selection.” Journal of Open Source Software, 6(59), 3010. doi:10.21105/joss.03010 .

Examples

set.seed(1)
sets = list(
  sample(letters[1:3], 1),
  sample(letters[1:3], 2)
)
jaccard(sets)
#> [1] 0.5