Canberra distance

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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] It has also been used to analyze the gut microbiome in different disease states.[5]

Definition[edit]

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[edit]

Notes[edit]

  1. ^ Lance, G. N.; Williams, W. T. (1966). "Computer programs for hierarchical polythetic classification ("similarity analysis")". Computer Journal. 9 (1): 60–64. doi:10.1093/comjnl/9.1.60.
  2. ^ Lance, G. N.; Williams, W. T. (1967). "Mixed-data classificatory programs I.) Agglomerative Systems". Australian Computer Journal: 15–20.
  3. ^ a b 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. ^ 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.
  5. ^ Hill-Burns, EM; Debelius, JW; Morton, JT; Wissemann, WT; Lewis, MR; Wallen, ZD; Peddada, SD; Factor, SA; Molho, E; Zabetian, CP; Knight, R; Payami, H (May 2017). "Parkinson's disease and Parkinson's disease medications have distinct signatures of the gut microbiome". Movement disorders : official journal of the Movement Disorder Society. 32 (5): 739–749. doi:10.1002/mds.26942. PMID 28195358.

References[edit]