Biweight midcorrelation

In statistics, biweight midcorrelation (also called bicor) is a measure of similarity between samples. It is median-based, rather than mean-based, thus is less sensitive to outliers, and can be a robust alternative to other similarity metrics, such as Pearson correlation or mutual information.[1]

Derivation

edit

Here we find the biweight midcorrelation of two vectors   and  , with   items, representing each item in the vector as   and  . First, we define   as the median of a vector   and   as the median absolute deviation (MAD), then define   and   as,

 

Now we define the weights   and   as,

 

where   is the identity function where,

 

Then we normalize so that the sum of the weights is 1:

 

Finally, we define biweight midcorrelation as,

 

Applications

edit

Biweight midcorrelation has been shown to be more robust in evaluating similarity in gene expression networks,[2] and is often used for weighted correlation network analysis.

Implementations

edit

Biweight midcorrelation has been implemented in the R statistical programming language as the function bicor as part of the WGCNA package[3]

Also implemented in the Raku programming language as the function bi_cor_coef as part of the Statistics module.[4]

References

edit
  1. ^ Wilcox, Rand (January 12, 2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press. p. 455. ISBN 978-0123869838.
  2. ^ Song, Lin (9 December 2012). "Comparison of co-expression measures: mutual information, correlation, and model based indices". BMC Bioinformatics. 13 (328): 328. doi:10.1186/1471-2105-13-328. PMC 3586947. PMID 23217028.
  3. ^ Langfelder, Peter. "WGCNA: Weighted Correlation Network Analysis (an R package)". CRAN. Retrieved 2018-04-06.
  4. ^ Khanal, Suman. "Statistics: Raku module for doing statistics". GitHub. Retrieved 2022-03-11.