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{{Geometry-stub}}
The '''Canberra distance''' is a numerical measure of the distance between pairs of points in a [[vector space]], introduced in 1966<ref>{{cite journal|last1=Lance|first1=G. N.|last2=Williams|first2=W. T.|author2-link=W. T. Williams|title=Computer programs for hierarchical polythetic classification ("similarity analysis").|journal=Computer Journal|year=1966|volume=9|issue=1|pages=60–64|accessdate=18 October 2011|doi=10.1093/comjnl/9.1.60}}</ref>
and refined in 1967<ref name=Lance>{{cite journal|last1=Lance|first1=G. N.|last2=Williams|first2=W. T.|author2-link=W. T. Williams|title=Mixed-data classificatory programs I.) Agglomerative Systems|journal=Australian Computer Journal|year=1967|pages=15–20|accessdate=18 October 2011}}</ref> by G. N. Lance and [[W. T. Williams]]. It is a weighted version of [[Manhattan distance|''L''₁ (Manhattan) distance]].<ref name="jurman">Jurman G, Riccadonna S, Visintainer R, Furlanello C: Canberra Distance on Ranked Lists. In Proceedings, Advances in Ranking – NIPS 09 Workshop Edited by Agrawal S, Burges C, Crammer K. 2009, 22–27.</ref>
The Canberra distance has been used as a metric for comparing [[ranked list]]s<ref name="jurman"/> and for [[intrusion detection]] in [[computer security]].<ref>Syed Masum Emran and Nong Ye (2002). Robustness of chi-square and Canberra distance metrics for computer intrusion detection. ''[[Quality and Reliability Engineering International]]'' '''18''':19–28.</ref>

== Definition ==
The Canberra distance ''d'' between vectors '''p''' and '''q''' in an ''n''-dimensional [[real number|real]] [[vector space]] is given as follows:
:<math>d(\mathbf{p}, \mathbf{q}) = \sum_{i=1}^n \frac{|p_i-q_i|}{|p_i|+|q_i|},</math>

where
:<math>\mathbf{p}=(p_1,p_2,\dots,p_n)\text{ and }\mathbf{q}=(q_1,q_2,\dots,q_n)\,</math>
are [[Euclidean vector|vector]]s.

==See also==
*[[Normed vector space]]
*[[Metric (mathematics)|Metric]]
*[[Manhattan distance]]

==Notes==
{{Reflist}}

==References ==
* {{cite web|last=Schulz|first=Jan|title=Canberra distance|url=http://www.code10.info/index.php?option=com_content&view=article&id=49:article_canberra-distance&catid=38:cat_coding_algorithms_data-similarity&Itemid=57|work=Code 10|accessdate=18 October 2011}}



[[Category:Digital geometry]]
[[Category:Metric geometry]]
[[Category:Norms (mathematics)]]

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en>ChrisGualtieri: Remove stub template(s). Page is start class or higher. Also check for and do General Fixes + Checkwiki fixes using AWB