\name{adjacency.polyReg}
\alias{adjacency.polyReg}
%- Also NEED an '\alias' for EACH other topic documented here.
\title{Adjacency matrix based on polynomial regression
}
\description{
adjacency.polyReg calculates a network adjacency matrix by fitting polynomial regression models to pairs of variables (i.e. pairs of columns from
 \code{datExpr}). Each polynomial fit results in a model fitting index R.squared. 
Thus, the n columns of  \code{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 \code{symmetrizationMethod}.}
\usage{
adjacency.polyReg(datExpr, degree=3, symmetrizationMethod = "mean")
}
%- maybe also 'usage' for other objects documented here.
\arguments{
  \item{datExpr}{data frame containing numeric variables. Example: Columns may correspond to genes and rows to observations (samples).}
  \item{degree}{
the degree of the polynomial. Must be less than the number of unique points.}
  \item{symmetrizationMethod}{character string (eg "none", "min","max","mean") that specifies the method used to symmetrize the pairwise model fitting index matrix (see details).}
}
\details{
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 \code{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 polynomial regression model glm(y ~ poly(x,degree))  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 polynomial 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). If \code{degree}>1 then 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 \code{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)). 
\code{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)).
}
\value{
An adjacency matrix of dimensions ncol(datExpr) times ncol(datExpr).}
\references{
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

}
\author{
Lin Song, Steve Horvath 
}

\seealso{
For more information about polynomial regression, please refer to functions 
\code{\link{poly}} and \code{\link{glm}}
}
\examples{
#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.polyReg(datE, symmetrizationMethod="max")
A.max
#calculate adjacency by symmetrizing using max
A.mean=adjacency.polyReg(datE, symmetrizationMethod="mean")
A.mean
# output the unsymmetrized pairwise model fitting indices R.squared 
R.squared=adjacency.polyReg(datE, symmetrizationMethod="none")
R.squared
}


\keyword{misc}% __ONLY ONE__ keyword per line
