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DiceDissimilarity[x,y]

gives the Dice dissimilarity between Boolean vectors x and y.

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DiceDissimilarity

DiceDissimilarity[x,y]

gives the Dice dissimilarity between Boolean vectors x and y.

Details

  • DiceDissimilarity works for both True, False vectors and 0, 1 vectors.
  • DiceDissimilarity[u,v] is equivalent to (n10+n01)/(2n11+n10+n01), where nij is the number of corresponding pairs of elements in u and v respectively equal to i and j.

Examples

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Basic Examples  (2)

Dice dissimilarity between two 0, 1 vectors:

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

Dice dissimilarity between two Boolean vectors:

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

Scope  (2)

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

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

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

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

Applications  (2)

Cluster binary data using Dice dissimilarity:

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

Cluster True, False data using Dice dissimilarity:

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

Properties & Relations  (4)

Dice dissimilarity is bounded by 0 and 1:

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

DiceDissimilarity is less than or equal to JaccardDissimilarity:

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

DiceDissimilarity is less than or equal to SokalSneathDissimilarity:

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

DiceDissimilarity is less than or equal to RussellRaoDissimilarity:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_dicedissimilarity, author="Wolfram Research", title="{DiceDissimilarity}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/DiceDissimilarity.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_dicedissimilarity, organization={Wolfram Research}, title={DiceDissimilarity}, year={2007}, url={https://reference.wolfram.com/language/ref/DiceDissimilarity.html}, note=[Accessed: 13-June-2026]}