Canberra distance
From HandWiki
Short description: Measure of distance between vectors
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 Godfrey N. Lance and William 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] It has also been used to analyze the gut microbiome in different disease states.[5]
Definition
The Canberra distance d between vectors p and q in an n-dimensional real vector space is given as follows:
- [math]\displaystyle{ d(\mathbf{p}, \mathbf{q}) = \sum_{i=1}^n \frac{|p_i-q_i|}{|p_i|+|q_i|} }[/math]
where
- [math]\displaystyle{ \mathbf{p}=(p_1,p_2,\dots,p_n)\text{ and }\mathbf{q}=(q_1,q_2,\dots,q_n) }[/math]
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.[citation needed]
See also
- Normed vector space
- Metric
- Manhattan distance
Notes
- ↑ Lance, Godfrey N.; Williams, William T. (1966). "Computer programs for hierarchical polythetic classification ("similarity analysis")". Computer Journal 9 (1): 60–64. doi:10.1093/comjnl/9.1.60.
- ↑ Lance, Godfrey N.; Williams, William T. (1967). "Mixed-data classificatory programs I.) Agglomerative Systems". Australian Computer Journal: 15–20.
- ↑ 3.0 3.1 Giuseppe Jurman; Samantha Riccadonna; Roberto Visintainer; Cesare Furlanello; "Canberra Distance on Ranked Lists", in Shivani Agrawal; Chris Burges; Koby Crammer (editors); Proceedings, Advances in Ranking – NIPS 09 Workshop, 2009, p. 22–27
- ↑ Emran, Syed Masum; Ye, Nong (2002). "Robustness of chi-square and Canberra distance metrics for computer intrusion detection". Quality and Reliability Engineering International 18 (1): 19–28. doi:10.1002/qre.441.
- ↑ Hill-Burns, Erin M.; Debelius, Justine W.; Morton, James T.; Wissemann, William T.; Lewis, Matthew R.; Wallen, Zachary D.; Peddada, Shyamal D.; Factor, Stewart A. et al. (May 2017). "Parkinson's disease and Parkinson's disease medications have distinct signatures of the gut microbiome". Movement Disorders 32 (5): 739–749. doi:10.1002/mds.26942. PMID 28195358.
References
- Schulz, Jan. "Canberra distance". Code 10. 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. Retrieved 18 October 2011.
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