Signal-to-noise statistic

{{One source|date=August 2010}}

In mathematics the signal-to-noise statistic distance between two vectors a and b with mean values $\backslash mu\; \_a$ and $\backslash mu\; \_b$ and standard deviation $\backslash sigma\; \_a$ and $\backslash sigma\; \_b$ respectively is:

:$D\_\{sn\}\; =\; \{(\backslash mu\; \_a\; -\; \backslash mu\; \_b)\; \backslash over\; (\backslash sigma\; \_a\; +\; \backslash sigma\; \_b)\}$

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.Auffarth, B., Lopez, M., Cerquides, J. (2010). [https://www.researchgate.net/publication/225143114_Comparison_of_Redundancy_and_Relevance_Measures_for_Feature_Selection_in_Tissue_Classification_of_CT_Images Comparison of redundancy and relevance measures for feature selection in tissue classification of CT images]. Advances in Data Mining. Applications and Theoretical Aspects. p. 248--262. Springer.

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.Golub, T.R. et al. (1999) [http://archive.broadinstitute.org/mpr/publications/projects/Leukemia/Golub_et_al_1999.pdf Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring]. Science 286, 531-537,Slonim D.K. et al. (2000) [https://www.researchgate.net/publication/2804500_Class_Prediction_and_Discovery_Using_Gene_Expression_Data Class Prediction and Discovery Using Gene Expression Data]. Procs. of the Fourth Annual International Conference on Computational Molecular Biology Tokyo, Japan April 8 - 11, p263-272Pomeroy, S.L. et al. (2002) [http://www.broad.mit.edu/mpr/CNS/ Gene Expression-Based Classification and Outcome Prediction of Central Nervous System Embryonal Tumors]. Nature 415, 436–442.