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\name{em}
\alias{em}
\title{EM algorithm starting with E-step for parameterized Gaussian mixture models}
\description{
Implements the EM algorithm for parameterized Gaussian mixture models,
starting with the expectation step.
}
\usage{
em(data, modelName, parameters, prior = NULL, control = emControl(),
warn = NULL, \dots)
}
\arguments{
\item{data}{
A numeric vector, matrix, or data frame of observations. Categorical
variables are not allowed. If a matrix or data frame, rows
correspond to observations and columns correspond to variables.
}
\item{modelName}{
A character string indicating the model. The help file for
\code{\link{mclustModelNames}} describes the available models.
}
\item{parameters}{
A names list giving the parameters of the model.
The components are as follows:
\describe{
\item{\code{pro}}{
Mixing proportions for the components of the mixture.
If the model includes a Poisson term for noise, there
should be one more mixing proportion than the number
of Gaussian components.
}
\item{\code{mean}}{
The mean for each component. If there is more than one component,
this is a matrix whose kth column is the mean of the \emph{k}th
component of the mixture model.
}
\item{\code{variance}}{
A list of variance parameters for the model.
The components of this list depend on the model
specification. See the help file for \code{\link{mclustVariance}}
for details.
}
\item{\code{Vinv}}{
An estimate of the reciprocal hypervolume of the data region.
If set to NULL or a negative value, the default is determined by
applying function \code{hypvol} to the data.
Used only when \code{pro} includes an additional
mixing proportion for a noise component.
}
}
}
\item{prior}{
Specification of a conjugate prior on the means and variances.
The default assumes no prior.
}
\item{control}{
A list of control parameters for EM. The defaults are set by the call
\code{emControl()}.
}
\item{warn}{
A logical value indicating whether or not a warning should be issued
when computations fail. The default is \code{warn=FALSE}.
}
\item{\dots}{
Catches unused arguments in indirect or list calls via \code{do.call}.
}
}
\value{
A list including the following components:
\item{modelName}{
A character string identifying the model (same as the input argument).
}
\item{n}{
The number of observations in the data.
}
\item{d}{
The dimension of the data.
}
\item{G}{
The number of mixture components.
}
\item{z}{
A matrix whose \code{[i,k]}th entry is the
conditional probability of the \emph{i}th observation belonging to
the \emph{k}th component of the mixture.
}
\item{parameters}{
\describe{
\item{\code{pro}}{
A vector whose \emph{k}th component is the mixing proportion for
the \emph{k}th component of the mixture model.
If the model includes a Poisson term for noise, there
should be one more mixing proportion than the number
of Gaussian components.
}
\item{\code{mean}}{
The mean for each component. If there is more than one component,
this is a matrix whose kth column is the mean of the \emph{k}th
component of the mixture model.
}
\item{\code{variance}}{
A list of variance parameters for the model.
The components of this list depend on the model
specification. See the help file for \code{\link{mclustVariance}}
for details.
}
\item{\code{Vinv}}{
The estimate of the reciprocal hypervolume of the data region
used in the computation when the input indicates the
addition of a noise component to the model.
}
}
}
\item{loglik}{
The log likelihood for the data in the mixture model.
}
\item{control}{
The list of control parameters for EM used.
}
\item{prior}{
The specification of a conjugate prior on the means and variances used,
\code{NULL} if no prior is used.
}
\item{Attributes:}{
\code{"info"} Information on the iteration.\cr
\code{"WARNING"} An appropriate warning if problems are
encountered in the computations.
}
}
\seealso{
\code{\link{emE}}, \dots,
\code{\link{emVVV}},
\code{\link{estep}},
\code{\link{me}},
\code{\link{mstep}},
\code{\link{mclust.options}},
\code{\link{do.call}}
}
\examples{
\donttest{
msEst <- mstep(modelName = "EEE", data = iris[,-5],
z = unmap(iris[,5]))
names(msEst)
em(modelName = msEst$modelName, data = iris[,-5],
parameters = msEst$parameters)
do.call("em", c(list(data = iris[,-5]), msEst)) ## alternative call
}
}
\keyword{cluster}
|
