Calculation of the topological overlap matrix from given expression data.
TOMsimilarityFromExpr(
datExpr,
weights = NULL,
corType = "pearson",
networkType = "unsigned",
power = 6,
TOMType = "signed",
TOMDenom = "min",
maxPOutliers = 1,
quickCor = 0,
pearsonFallback = "individual",
cosineCorrelation = FALSE,
replaceMissingAdjacencies = FALSE,
suppressTOMForZeroAdjacencies = FALSE,
suppressNegativeTOM = FALSE,
useInternalMatrixAlgebra = FALSE,
nThreads = 0,
verbose = 1, indent = 0)expression data. A data frame in which columns are genes and rows ar samples. NAs are allowed, but not too many.
optional observation weights for datExpr to be used in correlation calculation.
A matrix of the same dimensions as
datExpr, containing non-negative weights.
character string specifying the correlation to be used. Allowed values are (unique
abbreviations of) "pearson" and "bicor", corresponding to Pearson and bidweight
midcorrelation, respectively. Missing values are handled using the pairwise.complete.obs option.
network type. Allowed values are (unique abbreviations of) "unsigned",
"signed", "signed hybrid". See adjacency.
soft-thresholding power for netwoek construction.
one of "none", "unsigned", "signed", "signed Nowick",
"unsigned 2", "signed 2" and "signed Nowick 2". If "none", adjacency
will be used for clustering. See details and keep in mind that the "2" versions should be considered experimental and are
subject to change.
a character string specifying the TOM variant to be used. Recognized values are
"min" giving the standard TOM described in Zhang and Horvath (2005), and "mean" in which
the min function in the denominator is replaced by mean. The "mean" may produce
better results but at this time should be considered experimental.
only used for corType=="bicor". 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 maxPOutliers is considered an outlier by the weight function based on
9*mad(x), the width of the weight function is increased such that the percentile of outliers on
that side of the median equals maxPOutliers. Using maxPOutliers=1 will effectively disable
all weight function broadening; using maxPOutliers=0 will give results that are quite similar (but
not equal to) Pearson correlation.
real number between 0 and 1 that controls the handling of missing data in the calculation of correlations. See details.
Specifies whether the bicor calculation, if used, should revert to Pearson when median
absolute deviation (mad) is zero. Recongnized values are (abbreviations of)
"none", "individual", "all". If set to
"none", zero mad will result in NA for the corresponding correlation.
If set to "individual", Pearson calculation will be used only for columns that have zero mad.
If set to "all", the presence of a single zero mad will cause the whole variable to be treated in
Pearson correlation manner (as if the corresponding robust option was set to FALSE). Has no
effect for Pearson correlation. See bicor.
logical: should the cosine version of the correlation calculation be used? The cosine calculation differs from the standard one in that it does not subtract the mean.
logical: should missing values in the calculation of adjacency be replaced by 0?
Logical: should the result be set to zero for zero adjacencies?
Logical: should the result be set to zero when negative?
Logical: should WGCNA's own, slow, matrix multiplication be used instead of R-wide BLAS? Only useful for debugging.
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.
integer level of verbosity. Zero means silent, higher values make the output progressively more and more verbose.
indentation for diagnostic messages. Zero means no indentation, each unit adds two spaces.
A matrix holding the topological overlap.
Several alternate definitions of topological overlap are available. The oldest version is now called "unsigned"; in this version, all adjacencies are assumed to be non-negative and the topological overlap of nodes \(i,j\) is given by
$$TOM_{ij} = \frac{a_{ij} + \sum_{k\neq i,j} a_{ik}a_{kj} }{f(k_i, k_j) + 1 - a_{ij}} \, ,$$
where the sum is over \(k\) not equal to either \(i\) or \(j\), the function \(f\) in the denominator can be
either min or mean (goverened by argument TOMDenom), and \(k_i = \sum_{j\neq i} a_{ij}\) is
the connectivity of node \(i\). The signed versions assume that the adjacency matrix was obtained from an underlying
correlation matrix, and the element \(a_{ij}\) carries the sign of the underlying correlation of the two
vectors. (Within WGCNA, this can really only apply to the unsigned adjacency since signed adjacencies are (essentially)
zero when the underlying correlation is negative.) The signed and signed Nowick versions are similar to the above unsigned
version, differing only in absolute
values placed in the expression: the signed Nowick expression is
$$TOM_{ij} = \frac{a_{ij} + \sum_{k\neq i,j} a_{ik}a_{kj} }{f(k_i, k_j) + 1 - |a_{ij}|} \, .$$
This TOM lies between -1 and 1, and typically is negative when the underlying adjacency is negative. The signed TOM is simply the absolute value of the signed Nowick TOM and is hence always non-negative. For non-negative adjacencies, all 3 version give the same result.
A brief note on terminology: the original article by Nowick et al use the name "weighted TO" or wTO; since all of the topological overlap versions calculated in this function are weighted, we use the name signed to indicate that this TOM keeps track of the sign of the underlying correlation.
The "2" versions of all 3 adjacency types have a somewhat different form in which the adjacency and the product are normalized separately. Thus, the "unsigned 2" version is
$$TOM^{(2)}_{ij} = \frac{1}{2}\left[a_{ij} + \frac{\sum_{k\neq i,j} a_{ik}a_{kj} }{f(k_i, k_j) - a_{ij}}\right] \, .$$
At present the relative weight of the adjacency and the normalized product term are equal and fixed; in the future a user-specified or automatically determined weight may be implemented. The "signed Nowick 2" and "signed 2" are defined analogously to their original versions. The adjacency is assumed to be signed, and the expression for "signed Nowick 2" TOM is
$$TOM^{(2)}_{ij} = \frac{1}{2}\left[a_{ij} + \frac{\sum_{k\neq i,j} a_{ik}a_{kj} }{f(k_i, k_j) - |a_{ij}| } \right] \, .$$
Analogously to "signed" TOM, "signed 2" differs from "signed Nowick 2" TOM only in taking the absolute value of the result.
At present the "2" versions should all be considered experimental and are subject to change.
Bin Zhang and Steve Horvath (2005) "A General Framework for Weighted Gene Co-Expression Network Analysis", Statistical Applications in Genetics and Molecular Biology: Vol. 4: No. 1, Article 17