# Metric Function

A Metric Function is a measure function that maps two or more items to a numeric value that represents the distance value between them.

**Context:**- It can be used to make Choices.
- It can range from being a Similarity Metric to being a Distance Metric, if it does not/does abide by a triangle inequality.

**Example(s):**- a Distance Metric, such as a Euclidean distance metric.
- an F1 Metric.
- a Space Complexity Metric.
- a Reference Certainty Metric.
- a Performance Metric (can be Compared against some baseline)
- a Computational Complexity Metric.
- …

**Counter-Example(s):****See:**Scale, Scalar Function.

## Reference

### 2014

- http://en.wikipedia.org/wiki/Metric_%28mathematics%29
- In mathematics, a
**metric**or**distance function**is a function that defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable.In differential geometry, the word "metric" may refer to a bilinear form that may be defined from the tangent vectors of a differentiable manifold onto a scalar, allowing distances along curves to be determined through integration. It is more properly termed a metric tensor.

- In mathematics, a

### 2012

- (Wikipedia, 2012) ⇒ http://en.wikipedia.org/wiki/Metric_(mathematics)
- QUOTE: In mathematics, a
**metric space**is a set where a notion of distance (called a metric) between elements of the set is defined.The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion of "metric" is a generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line segment connecting them.

Non-intuitive metric spaces occur in elliptic geometry and hyperbolic geometry. For example, the hyperboloid model of hyperbolic geometry is used in special relativity for a metric space of velocities.

A metric space also induces topological properties like open and closed sets which leads to the study of even more abstract topological spaces.

- QUOTE: In mathematics, a

### 2009

- WordNet
- metric function: a function of a topological space that gives, for any two points in the space, a value equal to the distance between them
- based on the meter as a standard of measurement; "the metric system"; "metrical equivalents"
- metric unit: a decimal unit of measurement of the metric system (based on meters and kilograms and seconds); "convert all the measurements to metric units"; "it is easier to work in metric"
- system of measurement: a system of related measures that facilitates the quantification of some particular characteristic
- measured: the rhythmic arrangement of syllables

- http://www.nature.com/nrg/journal/v5/n11/glossary/nrg1469_glossary.html
- A measure of similarity or dissimilarity that can be used to organize groups according to their degree of relation to one another. ...