\name{extractPlot}
\alias{extractPlot}
\title{Plotting of Biclustering Results}
\description{

  \code{extractPlot}: \R implementation of  \code{extractPlot}.
}
\usage{

extractPlot(fact,thresZ=0.5,ti="",thresL=NULL,Y=NULL,which=c(1,2,3,4,5,6,7,8))

}
\arguments{
  \item{fact}{object of the class \code{Factorization}.}
  \item{thresZ}{threshold for sample belonging to bicluster; default 0.5.}
  \item{thresL}{threshold for loading belonging to bicluster (estimated
    if not given).}
  \item{ti}{plot title; default "".}
  \item{Y}{noise free data matrix.}
  \item{which}{which plot is shown: 1=noise free data (if available),
    2=data, 3=reconstructed data, 4=error, 5=absolute factors,
    6=absolute loadings, 7=reconstructed matrix sorted,8=original matrix
    sorted; default c(1,2,3,4,5,6,7,8).}

}
\details{

  Essentially the model is the sum of
  outer products of vectors:
   \deqn{X  =  \sum_{i=1}^{p} \lambda_i  z_i^T  +  U}
  where the number of summands  \eqn{p}
  is the number of biclusters.
  The matrix factorization is
  \deqn{X  =  L  Z  +  U}
  

   Here \eqn{\lambda_i} are from \eqn{R^n}, \eqn{z_i} from
   \eqn{R^l}, \eqn{L} from \eqn{R^{n \times p}},
   \eqn{Z} from \eqn{R^{p \times l}}, and \eqn{X}, \eqn{U}
   from \eqn{R^{n \times l}}.
   
   The hidden dimension \eqn{p} is used for kmeans clustering of
   \eqn{\lambda_i} and \eqn{z_i }.

   The \eqn{\lambda_i } and \eqn{z_i } are used to
   extract the bicluster \eqn{i}, where a threshold determines which
   observations and which samples belong the the bicluster.

   The method produces following plots depending what plots are chosen
   by the "which" variable:

   \dQuote{Y}: noise free data (if available),
   \dQuote{X}: data,
   \dQuote{LZ}: reconstructed data,
   \dQuote{LZ-X}: error,
   \dQuote{abs(Z)}: absolute factors,
   \dQuote{abs(L)}: absolute loadings,
   \dQuote{pmL*L*z*pmZ}: reconstructed matrix sorted,
   \dQuote{pmL*X*pmZ}: original matrix sorted.

   For sorting first \code{kmeans} is performed
   on the \eqn{p} dimensional space and then the vectors
   which belong to the same cluster are put together.
   
   This sorting is in general not able to 
   visualize all biclusters as blocks if they overlap.

   The kmeans clusters are given by \code{biclust} with
   components \code{biclustx} (the clustered observations)
   and \code{biclusty} (the clustered samples).

  Implementation in \R.
}
\seealso{
\code{\link{fabia}},
\code{\link{fabias}},
\code{\link{fabiap}},
\code{\link{fabi}},
\code{\link{fabiasp}},
\code{\link{spfabia}},
\code{\link{mfsc}},
\code{\link{nmfdiv}},
\code{\link{nmfeu}},
\code{\link{nmfsc}},
\code{\link{plot}},
\code{\link{extractPlot}},
\code{\link{extractBic}},
\code{\link{plotBicluster}},
\code{\link{Factorization}},
\code{\link{projFuncPos}},
\code{\link{projFunc}},
\code{\link{estimateMode}},
\code{\link{makeFabiaData}},
\code{\link{makeFabiaDataBlocks}},
\code{\link{makeFabiaDataPos}},
\code{\link{makeFabiaDataBlocksPos}},
\code{\link{matrixImagePlot}},
\code{\link{summary}},
\code{\link{show}},
\code{\link{showSelected}},
\code{\link{fabiaDemo}},
\code{\link{fabiaVersion}}
}
\author{Sepp Hochreiter}
\examples{

#---------------
# TEST
#---------------

dat <- makeFabiaDataBlocks(n = 100,l= 50,p = 3,f1 = 5,f2 = 5,
  of1 = 5,of2 = 10,sd_noise = 3.0,sd_z_noise = 0.2,mean_z = 2.0,
  sd_z = 1.0,sd_l_noise = 0.2,mean_l = 3.0,sd_l = 1.0)

X <- dat[[1]]
Y <- dat[[2]]


resEx <- fabia(X,3,0.1,20)

extractPlot(resEx,ti="FABIA",Y=Y)



\dontrun{
#---------------
# DEMO1
#---------------

dat <- makeFabiaDataBlocks(n = 1000,l= 100,p = 10,f1 = 5,f2 = 5,
  of1 = 5,of2 = 10,sd_noise = 3.0,sd_z_noise = 0.2,mean_z = 2.0,
  sd_z = 1.0,sd_l_noise = 0.2,mean_l = 3.0,sd_l = 1.0)

X <- dat[[1]]
Y <- dat[[2]]


resToy <- fabia(X,13,0.01,200)

extractPlot(resToy,ti="FABIA",Y=Y)

#---------------
# DEMO2
#---------------

avail <- require(fabiaData)

if (!avail) {
    message("")
    message("")
    message("#####################################################")
    message("Package 'fabiaData' is not available: please install.")
    message("#####################################################")
} else {

data(Breast_A)

X <- as.matrix(XBreast)

resBreast <- fabia(X,5,0.1,200)

extractPlot(resBreast,ti="FABIA Breast cancer(Veer)")

#sorting of predefined labels
CBreast%*%rBreast$pmZ
}

}
}
\keyword{hplot}
\concept{biclustering}
\concept{sparse coding}
\concept{sparse matrix factorization}
\concept{non-negative matrix factorization}