In
mathematics the signal-to-noise statistic
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
between two
vectors ''a'' and ''b'' with
mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.
For a data set, the '' ari ...
values
and
and
standard deviation and
respectively is:
:
In the case of Gaussian-distributed data and unbiased class distributions, this statistic can be related to classification accuracy given an ideal linear discrimination, and a decision boundary can be derived.
This distance is frequently used to identify vectors that have significant difference. One usage is in
bioinformatics to locate
genes that are differential
expressed on
microarray experiments.
[Pomeroy, S.L. et al. (2002]
Gene Expression-Based Classification and Outcome Prediction of Central Nervous System Embryonal Tumors
Nature 415, 436–442.
See also
*
Distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
*
Uniform norm
In mathematical analysis, the uniform norm (or ) assigns to real- or complex-valued bounded functions defined on a set the non-negative number
:\, f\, _\infty = \, f\, _ = \sup\left\.
This norm is also called the , the , the , or, when th ...
*
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 ...
*
Signal-to-noise ratio
*
Signal to noise ratio (imaging)
Notes
Statistical distance
Statistical ratios
{{Statistics-stub