Signal-to-noise statistic
Encyclopedia
In mathematics
the signal-to-noise statistic distance
between two vectors a and b with mean
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 .
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
the signal-to-noise statistic distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...
between two vectors a and b with mean
Arithmetic mean
In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...
values
and and standard deviationStandard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
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
Bioinformatics
Bioinformatics is the application of computer science and information technology to the field of biology and medicine. Bioinformatics deals with algorithms, databases and information systems, web technologies, artificial intelligence and soft computing, information and computation theory, software...
to locate genes
Gênes
Gênes is the name of a département of the First French Empire in present Italy, named after the city of Genoa. It was formed in 1805, when Napoleon Bonaparte occupied the Republic of Genoa. Its capital was Genoa, and it was divided in the arrondissements of Genoa, Bobbio, Novi Ligure, Tortona and...
that are differential expressed
Gene expression
Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product. These products are often proteins, but in non-protein coding genes such as ribosomal RNA , transfer RNA or small nuclear RNA genes, the product is a functional RNA...
on microarray
Microarray
A microarray is a multiplex lab-on-a-chip. It is a 2D array on a solid substrate that assays large amounts of biological material using high-throughput screening methods.Types of microarrays include:...
experiments .
See also
- DistanceDistanceDistance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...
- Uniform norm
- Manhattan distance
- Signal-to-noise ratioSignal-to-noise ratioSignal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
- Signal to noise ratio (imaging)