# Canberra distance

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 *L*₁ (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.

## See also

## Notes

- ↑ 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. - ↑ Lance, G. N.; Williams, W. T. (1967). "Mixed-data classificatory programs I.) Agglomerative Systems".
*Australian Computer Journal*: 15–20. - 1 2 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.
- ↑ 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.

## References

- Schulz, Jan. "Canberra distance".
*Code 10*. Retrieved 18 October 2011.

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