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.

## 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
.

## See also

Package stabm which implements many more stability measures with included
correction for chance.

Other Similarity Measures:
`phi()`