\name{robustPca}
\alias{robustPca}
\title{PCA implementation based on robustSvd}
\usage{robustPca(Matrix, nPcs=2, verbose=interactive(), ...)}
\description{This is a PCA implementation robust to outliers in a data set. It
can also handle missing values, it is however NOT intended to be
used for missing value estimation.  As it is based on robustSVD we
will get an accurate estimation for the loadings also for
incomplete data or for data with outliers.  The returned scores
are, however, affected by the outliers as they are calculated
inputData X loadings. This also implies that you should look at
the returned R2/R2cum values with caution.  If the data show
missing values, scores are caluclated by just setting all NA -
values to zero. This is not expected to produce accurate results.
Please have also a look at the manual page for \code{robustSvd}.
Thus this method should mainly be seen as an attempt to integrate
\code{robustSvd()} into the framework of this package.  Use one of
the other methods coming with this package (like PPCA or BPCA) if
you want to do missing value estimation.  It is not recommended to
use this function directely but rather to use the pca() wrapper
function.}
\details{The method is very similar to the standard \code{prcomp()}
function.  The main difference is that \code{robustSvd()} is used
instead of the conventional \code{svd()} method.}
\value{Standard PCA result object used by all PCA-based methods
of this package. Contains scores, loadings, data mean and
more. See \code{\link{pcaRes}} for details.  are used.}
\seealso{\code{\link{robustSvd}, \link{svd}, \link{prcomp},
\link{pcaRes}}.}
\keyword{multivariate}
\author{Wolfram Stacklies}
\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 the number of components, which should resemble the internal
structure of the data.}
\item{verbose}{\code{boolean} Print some output to the command
line if TRUE}
\item{...}{Reserved for future use. Currently no further
parameters are used}}
\examples{## Load a complete sample metabolite data set and mean center the data
data(metaboliteDataComplete)
mdc <- scale(metaboliteDataComplete, center=TRUE, scale=FALSE)
## Now create 5\% of outliers.
cond   <- runif(length(mdc)) < 0.05;
mdcOut <- mdc
mdcOut[cond] <- 10
## Now we do a conventional PCA and robustPca on the original and the data
## with outliers.
## We use center=FALSE here because the large artificial outliers would
## affect the means and not allow to objectively compare the results.
resSvd    <- pca(mdc, method = "svd", nPcs = 10, center = FALSE)
resSvdOut <- pca(mdcOut, method = "svd", nPcs = 10, center = FALSE)
resRobPca <- pca(mdcOut, method = "robustPca", nPcs = 10, center = FALSE)
## Now we plot the results for the original data against those with outliers
## We can see that robustPca is hardly effected by the outliers.
plot(loadings(resSvd)[,1], loadings(resSvdOut)[,1])
plot(loadings(resSvd)[,1], loadings(resRobPca)[,1])}