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JaccardDissimilarity[u,v]

gives the Jaccard dissimilarity between Boolean vectors u and v.

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JaccardDissimilarity

JaccardDissimilarity[u,v]

gives the Jaccard dissimilarity between Boolean vectors u and v.

Details

Examples

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Basic Examples  (2)

Jaccard dissimilarity between two Boolean vectors:

Wolfram Language code: JaccardDissimilarity[{1, 0, 1, 1, 0}, {1, 1, 0, 1, 1}]

The elements can also be True and False:

Wolfram Language code: JaccardDissimilarity[{True, False, True}, {True, True, False}]

Scope  (2)

Compute dissimilarity between any 0, 1 vectors of equal length:

Wolfram Language code: JaccardDissimilarity[RandomInteger[1, 100], RandomInteger[1, 100]]

Compute dissimilarity between any True, False vectors of equal length:

Wolfram Language code: JaccardDissimilarity[RandomChoice[{True, False}, 1000], RandomChoice[{True, False}, 1000]]

Applications  (2)

Cluster 0, 1 data using Jaccard dissimilarity:

Wolfram Language code: FindClusters[{{0, 1}, {1, 1}, {0, 0}, {1, 0}}, DistanceFunction -> JaccardDissimilarity]

Cluster True, False data using Jaccard dissimilarity:

Wolfram Language code: FindClusters[{{False, True}, {True, True}, {False, False}, {True, False}}, DistanceFunction -> JaccardDissimilarity]

Properties & Relations  (5)

Jaccard dissimilarity is bounded by 0 and 1:

Wolfram Language code: JaccardDissimilarity[{1, 1, 1, 1}, {1, 1, 1, 1}]
Wolfram Language code: JaccardDissimilarity[{0, 0, 0, 0}, {1, 1, 1, 1}]

JaccardDissimilarity is greater than or equal to MatchingDissimilarity:

Wolfram Language code: u = RandomInteger[1, 100]; v = RandomInteger[1, 100];
Wolfram Language code: JaccardDissimilarity[u, v] ≥ MatchingDissimilarity[u, v]

JaccardDissimilarity is greater than or equal to DiceDissimilarity:

Wolfram Language code: u = RandomInteger[1, 100]; v = RandomInteger[1, 100];
Wolfram Language code: JaccardDissimilarity[u, v] ≥ DiceDissimilarity[u, v]

JaccardDissimilarity is less than or equal to SokalSneathDissimilarity:

Wolfram Language code: u = RandomInteger[1, 100]; v = RandomInteger[1, 100];
Wolfram Language code: JaccardDissimilarity[u, v] ≤ SokalSneathDissimilarity[u, v]

JaccardDissimilarity is less than or equal to RussellRaoDissimilarity:

Wolfram Language code: u = RandomInteger[1, 100]; v = RandomInteger[1, 100];
Wolfram Language code: JaccardDissimilarity[u, v] ≤ RussellRaoDissimilarity[u, v]
Wolfram Research (2007), JaccardDissimilarity, Wolfram Language function, https://reference.wolfram.com/language/ref/JaccardDissimilarity.html.

Text

Wolfram Research (2007), JaccardDissimilarity, Wolfram Language function, https://reference.wolfram.com/language/ref/JaccardDissimilarity.html.

CMS

Wolfram Language. 2007. "JaccardDissimilarity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/JaccardDissimilarity.html.

APA

Wolfram Language. (2007). JaccardDissimilarity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/JaccardDissimilarity.html

BibTeX

@misc{reference.wolfram_2026_jaccarddissimilarity, author="Wolfram Research", title="{JaccardDissimilarity}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/JaccardDissimilarity.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_jaccarddissimilarity, organization={Wolfram Research}, title={JaccardDissimilarity}, year={2007}, url={https://reference.wolfram.com/language/ref/JaccardDissimilarity.html}, note=[Accessed: 13-June-2026]}