Canberra distance


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 distance.
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 where Z is the number of attributes that are 0 for p and q.