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CanberraDistance[u,v]

给出向量 u 和 v 之间的 Canberra 距离.

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CanberraDistance

CanberraDistance[u,v]

给出向量 u 和 v 之间的 Canberra 距离.

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范例

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基本范例  (2)

两向量之间的 Canberra 距离：

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

两数字向量之间的 Canberra 距离：

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

范围  (2)

计算相同长度的任意向量之间的距离：

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

计算任意精度的向量之间的距离：

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

应用  (2)

用切比雪夫距离聚类数据：

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

证明三角不等式：

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]

属性和关系  (2)

Canberra 距离是尺度调整后的绝对差之和：

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 相当于尺度差的 Norm：

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 语言函数，https://reference.wolfram.com/language/ref/CanberraDistance.html.

文本

Wolfram Research (2007)，CanberraDistance，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CanberraDistance.html.

CMS

Wolfram 语言. 2007. "CanberraDistance." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/CanberraDistance.html.

APA

Wolfram 语言. (2007). CanberraDistance. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/CanberraDistance.html 年

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: 07-September-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: 07-September-2026]}