Signed distance function: Difference between revisions

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Clearly the definition of f given in the article means that \nabla f is the inward pointing normal
 
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In [[mathematics]] the '''signal-to-noise statistic''' [[distance]] between two [[vector (geometric)|vectors]] ''a'' and ''b'' with [[Arithmetic Mean|mean]] values <math>\mu _a</math> and <math>\mu _b</math> and [[standard deviation]] <math>\sigma _a</math> and <math>\sigma _b</math> respectively is:
 
:<math>D_{sn} = {(\mu _a - \mu _b) \over (\sigma _a + \sigma _b)}</math>
 
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.<ref>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</ref>
 
This distance is frequently used to identify vectors that have significant difference. One usage is in [[bioinformatics]] to locate [[genes]] that are differential [[Gene expression|expressed]] on [[microarray]] experiments.<ref>Pomeroy, S.L. et al. [http://www.broad.mit.edu/mpr/CNS/ Gene Expression-Based Classification and Outcome Prediction of Central Nervous System Embryonal Tumors]. Nature 415, 436–442.</ref>
 
==See also==
*[[Distance]]
*[[Uniform norm]]
*[[Manhattan distance]]
*[[Signal-to-noise ratio]]
*[[Signal to noise ratio (imaging)]]
 
==Notes==
{{Reflist}}
 
{{DEFAULTSORT:Signal-To-Noise Statistic}}
[[Category:Statistical distance measures]]
[[Category:Statistical ratios]]
 
 
{{Statistics-stub}}

Revision as of 13:01, 30 June 2013

Template:One source In mathematics the signal-to-noise statistic distance between two vectors a and b with mean values μa and μb and standard deviation σa and σb respectively is:

Dsn=(μa−μb)(σa+σb)

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]

See also

Notes

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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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