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\name{sigma2decomp}
\alias{sigma2decomp}
\title{
Convert mixture component covariances to decomposition form.
}
\description{
Converts a set of covariance matrices from representation as a 3-D array
to a parameterization by eigenvalue decomposition.
}
\usage{
sigma2decomp(sigma, G = NULL, tol = sqrt(.Machine$double.eps), \dots)
}
\arguments{
\item{sigma}{
Either a 3-D array whose [,,k]th component is the covariance matrix for the
kth component in an MVN mixture model, or a single covariance
matrix in the case that all components have the same covariance.
}
\item{G}{
The number of components in the mixture. When
\code{sigma} is a 3-D array, the number of components
can be inferred from its dimensions.
}
\item{tol}{
Tolerance for determining whether or not the covariances have equal volume,
shape, and or orientation. The default is the square root of the relative
machine precision, \code{sqrt(.Machine$double.eps)}, which is about
\code{1.e-8}.
}
\item{\dots}{
Catches unused arguments from an indirect or list call via \code{do.call}.
}
}
\value{
The covariance matrices for the mixture components in decomposition form,
including the following components:
\item{modelName}{
A character string indicating the infered model. The help file for
\code{\link{mclustModelNames}} describes the available models.
}
\item{d}{
The dimension of the data.
}
\item{G}{
The number of components in the mixture model.
}
\item{scale}{
Either a \emph{G}-vector giving the scale of the covariance (the
\emph{d}th root of its determinant) for each component in the
mixture model, or a single numeric value if the scale is the same
for each component.
}
\item{shape}{
Either a \emph{G} by \emph{d} matrix in which the \emph{k}th
column is the shape of the covariance matrix (normalized to have
determinant 1) for the \emph{k}th component, or a \emph{d}-vector
giving a common shape for all components.
}
\item{orientation}{
Either a \emph{d} by \emph{d} by \emph{G} array whose
\code{[,,k]}th entry is the orthonomal matrix whose columns are the
eigenvectors of the covariance matrix of the \emph{k}th component,
or a \emph{d} by \emph{d} orthonormal matrix if the mixture
components have a common orientation. The \code{orientation} component of
\code{decomp} can be omitted in spherical and diagonal models, for
which the principal components are parallel to the coordinate axes
so that the orientation matrix is the identity.
}
}
\seealso{
\code{\link{decomp2sigma}}
}
\examples{
meEst <- meEEE(iris[,-5], unmap(iris[,5]))
names(meEst$parameters$variance)
meEst$parameters$variance$Sigma
sigma2decomp(meEst$parameters$variance$Sigma, G = length(unique(iris[,5])))
}
\keyword{cluster}
|
