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
William T. Williams (born 1942) is an American painter and educator. He is known for his process-based approach to painting that engages motifs drawn from personal memory and cultural narrative to create non-referential, abstract compositions. ...
. It is a weighted version of
''L''₁ (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 list
A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked higher than", "ranked lower than" or "ranked equal to" the second.
In mathematics, this is known as a weak order or total preorder of o ...
s
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
References
*
Digital geometry
Metric geometry
Distance
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