The Canberra distance is a numerical measure of the distance between pairs of points in a
vector space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called '' vectors'', may be added together and multiplied ("scaled") by numbers called ''scalars''. Scalars are often real numbers, but can ...
, introduced in 1966
and refined in 1967
by Godfrey N. Lance and
William T. Williams. 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 lists
and for
intrusion detection
An intrusion detection system (IDS; also intrusion prevention system or IPS) is a device or software application that monitors a network or systems for malicious activity or policy violations. Any intrusion activity or violation is typically rep ...
in
computer security
Computer security, cybersecurity (cyber security), or information technology security (IT security) is the protection of computer systems and networks from attack by malicious actors that may result in unauthorized information disclosure, t ...
. It has also been used to analyze the
gut microbiome
Gut microbiota, gut microbiome, or gut flora, are the microorganisms, including bacteria, archaea, fungi, and viruses that live in the digestive tracts of animals. The gastrointestinal metagenome is the aggregate of all the genomes of the gut ...
in different disease states.
Definition
The Canberra distance ''d'' between vectors p and q in an ''n''-dimensional
real
Real may refer to:
Currencies
* Brazilian real (R$)
* Central American Republic real
* Mexican real
* Portuguese real
* Spanish real
* Spanish colonial real
Music Albums
* ''Real'' (L'Arc-en-Ciel album) (2000)
* ''Real'' (Bright album) (2010) ...
vector space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called '' vectors'', may be added together and multiplied ("scaled") by numbers called ''scalars''. Scalars are often real numbers, but can ...
is given as follows:
:
where
:
are
vector
Vector most often refers to:
*Euclidean vector, a quantity with a magnitude and a direction
*Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematic ...
s.
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
In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers, on which a norm is defined. A norm is the formalization and the generalization to real vector spaces of the intuitive notion of "length ...
*
Metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathem ...
*
Manhattan distance
A taxicab geometry or a Manhattan geometry is a geometry whose usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian co ...
Notes
References
*
Digital geometry
Metric geometry
Distance
{{metric-geometry-stub