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\name{rsc}
\alias{rsc}
\title{Robust and Sparse Correlation Matrix Estimator}
\description{
Compute the Robust and Sparse Correlation Matrix (RSC) estimator
proposed in Serra et al. (2018).
}
\usage{
rsc(cv, threshold = "minimum")
}
\arguments{
\item{cv}{
An S3 object of class \code{"rsc_cv"} (see \code{\link{rsc_cv}}).
}
\item{threshold}{
Threshold parameter to compute the RSC estimate. This
is a numeric value taken onto the interval (0,1), or it is
equal to \code{"minimum"} or \code{"minimum1se"} for selecting the
optimal threshold according to the selection performed in
\code{\link{rsc_cv}}.
}
}
\details{
The setting \code{threshold = "minimum"} or \code{threshold =
"minimum1se"} applies thresholding according to the criteria
discussed in the \emph{Details} section in \code{\link{rsc_cv}}.
When \code{cv} is obtained using \code{\link{rsc_cv}} with
\code{cv.type = "random"}, the default settings for \code{\link{rsc}}
implements exactly the RSC estimator proposed in Serra et al.,
(2018).
Although \code{threshold = "minimum"} is the default choice, in
high-dimensional situations \code{threshold = "minimum1se"} usually
provides a more parsimonious representation of the correlation
structure. Since the underlying RMAD matrix is passed through the
\code{cv} input, any other hand-tuned threshold to the RMAD matrix
can be applied without significant additional computational
costs. The latter can be done setting \code{threshold} to any value
onto the (0,1) interval.
The software is optimized to handle high-dimensional data sets,
therefore, the output RSC matrix is packed into a storage efficient
sparse format using the \code{"dsCMatrix"} S4 class from the
\code{\link{Matrix}} package. The latter is specifically designed for
sparse real symmetric matrices.
}
\value{
Returns a sparse correlaiton matrix of class \code{"dsCMatrix"}
(S4 class object) as defined in the \code{\link{Matrix}} package.
}
\section{References}{
Serra, A., Coretto, P., Fratello, M., and Tagliaferri, R. (2018).
Robust and sparsecorrelation matrix estimation for the analysis of
high-dimensional genomics data. \emph{Bioinformatics}, 34(4),
625-634. doi:10.1093/bioinformatics/btx642
}
\seealso{
\code{\link{rsc_cv}}
}
\examples{
\donttest{
## simulate a random sample from a multivariate Cauchy distribution
## note: example in high-dimension are obtained increasing p
set.seed(1)
n <- 100 # sample size
p <- 10 # dimension
dat <- matrix(rt(n*p, df = 1), nrow = n, ncol = p)
colnames(dat) <- paste0("Var", 1:p)
## perform 10-fold cross-validation repeated R=10 times
## note: for multi-core machines experiment with 'ncores'
set.seed(2)
a <- rsc_cv(x = dat, R = 10, K = 10)
a
## obtain the RSC matrix with "minimum" flagged solution
b <- rsc(cv = a, threshold = "minimum")
b
## obtain the RSC matrix with "minimum1se" flagged solution
d <- rsc(cv = a, threshold = "minimum1se")
d
## since the object 'a' stores the RMAD underlying estimator, we can
## apply thresholding at any level without re-estimating the RMAD
## matrix
e <- rsc(cv = a, threshold = 0.5)
e
}
}
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