\HeaderA{flexdaCMA}{Flexible Discriminant Analysis}{flexdaCMA}
\keyword{multivariate}{flexdaCMA}
\begin{Description}\relax
This method is experimental.

It is easy to show that, after appropriate scaling of the predictor matrix \code{X},
Fisher's Linear Discriminant Analysis is equivalent to Discriminant Analysis
in the space of the  fitted values from the linear regression of the
\code{nlearn x K} indicator matrix of the class labels on \code{X}.
This gives rise to 'nonlinear discrimant analysis' methods that expand
\code{X} in a suitable, more flexible basis. In order to avoid overfitting,
penalization is used. In the implemented version, the linear model is replaced
by a generalized additive one, using the package \code{mgcv}.

For \code{S4} method information, s. \code{\LinkA{flexdaCMA-methods}{flexdaCMA.Rdash.methods}}.
\end{Description}
\begin{Usage}
\begin{verbatim}
flexdaCMA(X, y, f, learnind, comp = 1, plot = FALSE, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{X}] Gene expression data. Can be one of the following:
\Itemize{
\item A \code{matrix}. Rows correspond to observations, columns to variables.
\item A \code{data.frame}, when \code{f} is \emph{not} missing (s. below).
\item An object of class \code{ExpressionSet}.
}

\item[\code{y}] Class labels. Can be one of the following:
\Itemize{
\item A \code{numeric} vector.
\item A \code{factor}.
\item A \code{character} if \code{X} is an \code{ExpressionSet} that
specifies the phenotype variable.
\item \code{missing}, if \code{X} is a \code{data.frame} and a
proper formula \code{f} is provided.
}
\bold{WARNING}: The class labels will be re-coded to
range from \code{0} to \code{K-1}, where \code{K} is the
total number of different classes in the learning set.

\item[\code{f}] A two-sided formula, if \code{X} is a \code{data.frame}. The
left part correspond to class labels, the right to variables.
\item[\code{learnind}] An index vector specifying the observations that
belong to the learning set. May be \code{missing};
in that case, the learning set consists of all
observations and predictions are made on the
learning set.
\item[\code{comp}] Number of discriminant coordinates (projections) to compute.
Default is one, must be smaller than or equal to \code{K-1}, where
\code{K} is the number of classes.
\item[\code{plot}] Should the projections onto the space spanned by the optimal
projection directions be plotted ? Default is \code{FALSE}.
\item[\code{...}] Further arguments passed to the function \code{gam} from
the package \code{mgcv}.
\end{ldescription}
\end{Arguments}
\begin{Value}
An object of class \code{\LinkA{cloutput}{cloutput}}.
\end{Value}
\begin{Note}\relax
Excessive variable selection has usually to performed before
\code{flexdaCMA} can be applied in the \code{p > n} setting.
Recall that the original predictor dimension is even enlarged,
therefore, it should be applied only with very few variables.
\end{Note}
\begin{Author}\relax
Martin Slawski \email{martin.slawski@campus.lmu.de}

Anne-Laure Boulesteix \url{http://www.slcmsr.net/boulesteix}
\end{Author}
\begin{References}\relax
Ripley, B.D. (1996)

Pattern Recognition and Neural Networks.

\emph{Cambridge University Press}
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{compBoostCMA}{compBoostCMA}}, \code{\LinkA{dldaCMA}{dldaCMA}}, \code{\LinkA{ElasticNetCMA}{ElasticNetCMA}},
\code{\LinkA{fdaCMA}{fdaCMA}}, \code{\LinkA{gbmCMA}{gbmCMA}},
\code{\LinkA{knnCMA}{knnCMA}}, \code{\LinkA{ldaCMA}{ldaCMA}}, \code{\LinkA{LassoCMA}{LassoCMA}},
\code{\LinkA{nnetCMA}{nnetCMA}}, \code{\LinkA{pknnCMA}{pknnCMA}}, \code{\LinkA{plrCMA}{plrCMA}},
\code{\LinkA{pls\_ldaCMA}{pls.Rul.ldaCMA}}, \code{\LinkA{pls\_lrCMA}{pls.Rul.lrCMA}}, \code{\LinkA{pls\_rfCMA}{pls.Rul.rfCMA}},
\code{\LinkA{pnnCMA}{pnnCMA}}, \code{\LinkA{qdaCMA}{qdaCMA}}, \code{\LinkA{rfCMA}{rfCMA}},
\code{\LinkA{scdaCMA}{scdaCMA}}, \code{\LinkA{shrinkldaCMA}{shrinkldaCMA}}, \code{\LinkA{svmCMA}{svmCMA}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
### load Golub AML/ALL data
data(golub)
### extract class labels
golubY <- golub[,1]
### extract gene expression from first 5 genes
golubX <- as.matrix(golub[,2:6])
### select learningset
ratio <- 2/3
set.seed(111)
learnind <- sample(length(golubY), size=floor(ratio*length(golubY)))
### run flexible Discriminant Analysis
result <- flexdaCMA(X=golubX, y=golubY, learnind=learnind, comp = 1)
### show results
show(result)
ftable(result)
plot(result)
\end{ExampleCode}
\end{Examples}

