Biweight Midcorrelation
Calculate biweight midcorrelation efficiently for matrices.
bicor(x, y = NULL,
robustX = TRUE, robustY = TRUE,
use = "all.obs",
maxPOutliers = 1,
quick = 0,
pearsonFallback = "individual",
cosine = FALSE,
cosineX = cosine,
cosineY = cosine,
nThreads = 0,
verbose = 0, indent = 0)x |
a vector or matrix-like numeric object |
y |
a vector or matrix-like numeric object |
robustX |
use robust calculation for |
robustY |
use robust calculation for |
use |
specifies handling of |
maxPOutliers |
specifies the maximum percentile of data that can be considered outliers on either
side of the median separately. For each side of the median, if
higher percentile than |
quick |
real number between 0 and 1 that controls the handling of missing data in the calculation of correlations. See details. |
pearsonFallback |
Specifies whether the bicor calculation should revert to Pearson when median
absolute deviation (mad) is zero. Recongnized values are (abbreviations of)
|
cosine |
logical: calculate cosine biweight midcorrelation? Cosine bicorrelation is similar to standard bicorrelation but the median subtraction is not performed. |
cosineX |
logical: use the cosine calculation for |
cosineY |
logical: use the cosine calculation for |
nThreads |
non-negative integer specifying the number of parallel threads to be used by certain parts of correlation calculations. This option only has an effect on systems on which a POSIX thread library is available (which currently includes Linux and Mac OSX, but excludes Windows). If zero, the number of online processors will be used if it can be determined dynamically, otherwise correlation calculations will use 2 threads. Note that this option does not affect what is usually the most expensive part of the calculation, namely the matrix multiplication. The matrix multiplication is carried out by BLAS routines provided by R; these can be sped up by installing a fast BLAS and making R use it. |
verbose |
if non-zero, the underlying C function will print some diagnostics. |
indent |
indentation for diagnostic messages. Zero means no indentation, each unit adds two spaces. |
This function implements biweight midcorrelation calculation (see references). If y is not
supplied, midcorrelation of columns of x will be calculated; otherwise, the midcorrelation between
columns of x and y will be calculated. Thus, bicor(x) is equivalent to
bicor(x,x) but is more efficient.
The options robustX, robustY allow the user to revert the calculation to standard
correlation calculation. This is important, for example, if any of the variables is binary
(or, more generally, discrete) as in such cases the robust methods produce meaningless results.
If both robustX, robustY are set to FALSE, the function calculates the
standard Pearson correlation (but is slower than the function cor).
The argument quick specifies the precision of handling of missing data in the correlation
calculations. Value quick = 0 will cause all
calculations to be executed accurately, which may be significantly slower than calculations without
missing data. Progressively higher values will speed up the
calculations but introduce progressively larger errors. Without missing data, all column meadians and
median absolute deviations (MADs) can be pre-calculated before the covariances are calculated. When
missing data are present,
exact calculations require the column medians and MADs to be calculated for each covariance. The
approximate calculation uses the pre-calculated median and MAD and simply ignores missing data in the
covariance calculation. If the number of missing data is high, the pre-calculated medians and MADs may
be very different from the actual ones, thus potentially introducing large errors.
The quick value times the
number of rows specifies the maximum difference in the
number of missing entries for median and MAD calculations on the one hand and covariance on the other
hand that will be tolerated before a recalculation is triggered. The hope is that if only a few missing
data are treated approximately, the error introduced will be small but the potential speedup can be
significant.
The choice "all" for pearsonFallback is not fully implemented in the sense that there are
rare but possible cases in which the calculation is equivalent to "individual". This may happen if
the use option is set to "pairwise.complete.obs" and
the missing data are arranged such that each individual mad is non-zero, but when two columns are analyzed
together, the missing data from both columns may make a mad zero. In such a case, the calculation is treated
as Pearson, but other columns will be treated as bicor.
A matrix of biweight midcorrelations. Dimnames on the result are set appropriately.
Peter Langfelder
Peter Langfelder, Steve Horvath (2012) Fast R Functions for Robust Correlations and Hierarchical Clustering. Journal of Statistical Software, 46(11), 1-17. https://www.jstatsoft.org/v46/i11/
"Dealing with Outliers in Bivariate Data: Robust Correlation", Rich Herrington, http://www.unt.edu/benchmarks/archives/2001/december01/rss.htm
"Introduction to Robust Estimation and Hypothesis Testing", Rand Wilcox, Academic Press, 1997.
"Data Analysis and Regression: A Second Course in Statistics", Mosteller and Tukey, Addison-Wesley, 1977, pp. 203-209.
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