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 1967L₁ (Manhattan) distance.[3]
The Canberra distance has been used as a metric for comparing
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:
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.[2][6]
See also
- Normed vector space
- Metric
- Manhattan distance
Notes
- .
- ^ a b Lance, Godfrey N.; Williams, William T. (1967). "Mixed-data classificatory programs I.) Agglomerative Systems". Australian Computer Journal: 15–20.
- ^ a b 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
- S2CID 122959778.
- PMID 28195358.
- .
References
- Schulz, Jan. "Canberra distance". Code 10. Retrieved 18 October 2011.