\name{nlpca}
\alias{nlpca}
\title{Non-linear PCA}
\description{Neural network based non-linear PCA}
\usage{nlpca(Matrix, nPcs=2, center=TRUE, completeObs=TRUE, maxSteps=2*prod(dim(Matrix)), unitsPerLayer=NULL, functionsPerLayer=NULL, weightDecay=0.001, weights=NULL, verbose=interactive(), ...)}
\arguments{
\item{Matrix}{\code{matrix} --- Data containing the variables in columns
  and observations in rows. The data may contain missing values, denoted as \code{NA}}
\item{nPcs}{\code{numeric} -- Number of components to estimate. The
  preciseness of the missing value estimation depends on thenumber of
  components, which should resemble the internal structure of the data.}
\item{center}{\code{boolean} Mean center the data if TRUE}
\item{completeObs}{\code{boolean} Return the complete observations if
  TRUE. This is the original data with NA values filled with the
  estimated values.}
\item{maxSteps}{\code{numeric} -- Number of estimation steps. Default is
  based on a generous rule of thumb.}
\item{unitsPerLayer}{The network units, example: c(2,4,6) for two input units 2feature units (principal components), one hidden layer fornon-linearity and three output units (original amount ofvariables).}
\item{functionsPerLayer}{The function to apply at each layer eg. c("linr", "tanh", "linr") }
\item{weightDecay}{Value between 0 and 1.}
\item{weights}{Starting weights for the network. Defaults to uniform
  random values but can be set specifically to make algorithm deterministic.}
\item{verbose}{\code{boolean} -- nlpca prints the number of steps and
  warning messages if set to TRUE. Default is interactive().}
\item{...}{Reserved for future use. Not passed on anywhere.}
}
\details{Artificial Neural Network (MLP) for performing non-linear PCA. Non-linear PCA is conceptually similar to classical PCA but
     theoretically quite different. Instead of simply decomposing our
     matrix (X) to scores (T) loadings (P) and an error (E) we train a
     neural network (our loadings) to find a curve through the
     multidimensional space of X that describes a much variance as
     possible. Classical ways of interpreting PCA results are thus not
     applicable to NLPCA since the loadings are hidden in the network.
     However, the scores of components that lead to low
     cross-validation errors can still be interpreted via the score
     plot.

     Unfortunately this method depend on slow iterations which
     currently are implemented in R only making this method extremely
     slow. Furthermore, the algorithm does not by itself decide when it
     has converged but simply does 'maxSteps' iterations.
   }
\value{\item{pcaRes}{Standard PCA result object used by all PCA-basedmethods of this package. Contains scores, loadings, data meanand more. See \code{\link{pcaRes}} for details.}
}
\references{Matthias Scholz, Fatma Kaplan, Charles L Guy, Joachim Kopkaand Joachim Selbig. Non-linear PCA: a missing dataapproach. \emph{Bioinformatics, 21(20):3887-3895, Oct 2005}}
\examples{
# Data set with three variables where data points constitute a helix
data(helix)
helixNA <- helix
helixNA <- t(apply(helix, 1, function(x) { x[sample(1:3, 1)] <- NA; x})) # not a single complete observation
helixNlPca <- pca(helixNA, nPcs=1, method="nlpca", maxSteps=1000)
fittedData <- fitted(helixNlPca, helixNA)
plot(fittedData[which(is.na(helixNA))], helix[which(is.na(helixNA))])
# compared to solution by Nipals PCA that cannot extract non-linear patterns
helixNipPca <- pca(helixNA, nPcs=2, method="nipals")
fittedData <- fitted(helixNipPca)
plot(fittedData[which(is.na(helixNA))], helix[which(is.na(helixNA))])
}
\author{Based on a matlab script by Matthias Scholz <matthias.scholz[at]uni-greifswald.de> and ported to R by HenningRedestig <redestig[at]mpimp-golm.mpg.de>}
\keyword{multivariate}