Biweight midcorrelation

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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]


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,


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.


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]


  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). 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.