The Canberra distance is a numerical measure of the distance between pairs of points in a vector space, introduced in 1966 and refined in 1967 by Godfrey N. Lance and William T. Williams. It is a weighted version of L₁ (Manhattan) distance.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 The Canberra distance has been used as a metric for comparing ranked lists and for intrusion detection in computer security. It has also been used to analyze the gut microbiome in different disease states.
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
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