Calculate network adjacency based on natural cubic spline regression
adjacency.splineReg calculates a network adjacency matrix by fitting spline regression models to pairs of variables (i.e. pairs of columns from
datExpr). Each spline regression model results in a fitting index R.squared. Thus, the n columns of
datExpr result in an n x n dimensional matrix whose entries contain R.squared measures. This matrix
is typically non-symmetric. To arrive at a (symmetric) adjacency matrix, one can specify different
symmetrization methods with symmetrizationMethod.
adjacency.splineReg( datExpr, df = 6-(nrow(datExpr)<100)-(nrow(datExpr)<30), symmetrizationMethod = "mean", ...)
datExpr |
data frame containing numeric variables. Example: Columns may correspond to genes and rows to observations (samples). |
df |
degrees of freedom in generating natural cubic spline. The default is as follows: if nrow(datExpr)>100 use 6, if nrow(datExpr)>30 use 4, otherwise use 5. |
symmetrizationMethod |
character string (eg "none", "min","max","mean") that specifies the method used to symmetrize the pairwise model fitting index matrix (see details). |
... |
other arguments from function |
A network adjacency matrix is a symmetric matrix whose entries lie between 0 and 1. It is a special case of a similarity matrix.
Each variable (column of datExpr) is regressed on every other variable, with each model fitting index recorded in a square matrix. Note that the model fitting index of regressing variable x and variable y is usually different from that of regressing y on x. From the spline regression model
glm( y ~ ns( x, df)) one can calculate the model fitting index R.squared(y,x).
R.squared(y,x) is a number between 0 and 1. The closer it is to 1, the better the spline regression model
describes the relationship between x and y and the more significant is the pairwise relationship between the
2 variables. One can also reverse the roles of x and y to arrive at a model fitting index R.squared(x,y).
R.squared(x,y) is typically different from R.squared(y,x). Assume a set of n variables x1,...,xn
(corresponding to the columns of datExpr) then one can define R.squared(xi,xj). The model fitting
indices for the elements of an n x n dimensional matrix (R.squared(ij)).
symmetrizationMethod implements the following symmetrization methods:
A.min(ij)=min(R.squared(ij),R.squared(ji)),
A.ave(ij)=(R.squared(ij)+R.squared(ji))/2,
A.max(ij)=max(R.squared(ij),R.squared(ji)).
For more information about natural cubic spline regression, please refer to functions "ns" and "glm".
An adjacency matrix of dimensions ncol(datExpr) times ncol(datExpr).
Lin Song, Steve Horvath
Song L, Langfelder P, Horvath S Avoiding mutual information based co-expression measures (to appear).
Horvath S (2011) Weighted Network Analysis. Applications in Genomics and Systems Biology. Springer Book. ISBN: 978-1-4419-8818-8
#Simulate a data frame datE which contains 5 columns and 50 observations m=50 x1=rnorm(m) r=.5; x2=r*x1+sqrt(1-r^2)*rnorm(m) r=.3; x3=r*(x1-.5)^2+sqrt(1-r^2)*rnorm(m) x4=rnorm(m) r=.3; x5=r*x4+sqrt(1-r^2)*rnorm(m) datE=data.frame(x1,x2,x3,x4,x5) #calculate adjacency by symmetrizing using max A.max=adjacency.splineReg(datE, symmetrizationMethod="max") A.max #calculate adjacency by symmetrizing using max A.mean=adjacency.splineReg(datE, symmetrizationMethod="mean") A.mean # output the unsymmetrized pairwise model fitting indices R.squared R.squared=adjacency.splineReg(datE, symmetrizationMethod="none") R.squared
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