Signal-to-noise statistic

In mathematics the signal-to-noise statistic distance between two vectors a and b with mean values $\mu _{a}$ and $\mu _{b}$ and standard deviation $\sigma _{a}$ and $\sigma _{b}$ respectively is:

D_{sn}={(\mu _{a}-\mu _{b}) \over (\sigma _{a}+\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.^[1]

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.^[2]

Notes

^ Auffarth, B., Lopez, M., Cerquides, J. (2010). 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. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.170.1528
^ Pomeroy, S.L. et al. Gene Expression-Based Classification and Outcome Prediction of Central Nervous System Embryonal Tumors. Nature 415, 436–442.

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[1] Auffarth, B., Lopez, M., Cerquides, J. (2010). 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. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.170.1528

[2] Pomeroy, S.L. et al. Gene Expression-Based Classification and Outcome Prediction of Central Nervous System Embryonal Tumors. Nature 415, 436–442.

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See also

Notes