- Definition
- See also
- Notes
- References
- External links
The Canberra distance is a numerical measure of the distance between pairs of points in a vector space, introduced in 1966[1]
and refined in 1967[2] by G. N. Lance and W. T. Williams. It is a weighted version of L₁ (Manhattan) distance.[3]
The Canberra distance has been used as a metric for comparing ranked lists[3] and for intrusion detection in computer security.[4]
Definition
The Canberra distance d between vectors p and q in an n-dimensional real vector space is given as follows:
where
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
Notes
1. ^{{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|doi=10.1093/comjnl/9.1.60}}
2. ^{{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}}
3. ^1 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.
4. ^{{cite journal |first=Syed Masum |last=Emran |first2=Nong |last2=Ye |year=2002 |title=Robustness of chi-square and Canberra distance metrics for computer intrusion detection |journal=Quality and Reliability Engineering International |volume=18 |issue=1 |pages=19–28 |doi=10.1002/qre.441 }}
2. ^{{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}}
3. ^1 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.
4. ^{{cite journal |first=Syed Masum |last=Emran |first2=Nong |last2=Ye |year=2002 |title=Robustness of chi-square and Canberra distance metrics for computer intrusion detection |journal=Quality and Reliability Engineering International |volume=18 |issue=1 |pages=19–28 |doi=10.1002/qre.441 }}
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}}
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2 : Digital geometry|Metric geometry
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