Canberra distance

Template:Short description The Canberra distance is a numerical measure of the distance between pairs of points in a vector space, introduced in 1966 and refined in 1967 by Godfrey N. Lance and William T. Williams. It is a weighted version of L₁ (Manhattan) distance. The Canberra distance has been used as a metric for comparing ranked lists and for intrusion detection in computer security. It has also been used to analyze the gut microbiome in different disease states.

Definition

The Canberra distance d between vectors p and q in an n-dimensional real vector space is given as follows:

$d(𝐩,𝐪)=\sum _{i=1}^n\frac{|p_i-q_i|}{|p_i|+|q_i|}$

where

$𝐩=(p_1,p_2,\dots ,p_n)\text{ and }𝐪=(q_1,q_2,\dots ,q_n)$

are vectors.

The Canberra metric, Adkins form, divides the distance d by (n-Z) where Z is the number of attributes that are 0 for p and q.

See also

• Normed vector space
• Metric
• Manhattan distance

References

• Template:Cite web

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