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CanberraDistance[u,v]

gives the Canberra distance between vectors u and v.

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CanberraDistance

CanberraDistance[u,v]

gives the Canberra distance between vectors u and v.

Details

Examples

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Basic Examples  (2)

Canberra distance between two vectors:

Wolfram Language code: CanberraDistance[{a, b, c}, {x, y, z}]

Canberra distance between numeric vectors:

Wolfram Language code: CanberraDistance[{1, 2, 3}, {2, 4, 6}]

Scope  (2)

Compute distance between any vectors of equal length:

Wolfram Language code: CanberraDistance[RandomReal[5, 100], RandomReal[5, 100]]

Compute distance between vectors of any precision:

Wolfram Language code: CanberraDistance[N[{1, 5, 2, 3, 10}, 50], N[{4, 15, 20, 5, 5}, 50]]

Applications  (2)

Cluster data using Canberra distance:

Wolfram Language code: FindClusters[{{2, 3}, {5, 10}, {4, 5}, {2, 2}}, DistanceFunction -> CanberraDistance]

Demonstrate the triangle inequality:

Wolfram Language code: d1 = CanberraDistance[{a, b}, {a, c}]
Wolfram Language code: d2 = CanberraDistance[{a, c}, {d, c}]
Wolfram Language code: d3 = CanberraDistance[{a, b}, {d, c}]
Wolfram Language code: Simplify[d3 <= d1 + d2]

Properties & Relations  (2)

Canberra distance is a sum of scaled absolute differences:

Wolfram Language code: CanberraDistance[{a, b, c}, {x, y, z}]
Wolfram Language code: Total[Abs[{a, b, c} - {x, y, z}] / (Abs[{a, b, c}] + Abs[{x, y, z}])]

CanberraDistance is equivalent to a Norm of scaled differences:

Wolfram Language code: u = {a, b, c}; v = {x, y, z};
Wolfram Language code: scaleddiff = (u - v) / (Abs[u] + Abs[v])
Wolfram Language code: Simplify[Norm[scaleddiff, 1]] == CanberraDistance[u, v]
Wolfram Research (2007), CanberraDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/CanberraDistance.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_canberradistance, author="Wolfram Research", title="{CanberraDistance}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/CanberraDistance.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_canberradistance, organization={Wolfram Research}, title={CanberraDistance}, year={2007}, url={https://reference.wolfram.com/language/ref/CanberraDistance.html}, note=[Accessed: 12-June-2026]}