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\name{hc}
\alias{hc}
\alias{print.hc}
\alias{as.hclust.hc}
\title{Model-based Agglomerative Hierarchical Clustering}
\description{
Agglomerative hierarchical clustering based on maximum likelihood criteria
for Gaussian mixture models parameterized by eigenvalue decomposition.
}
\usage{
hc(data,
modelName = "VVV",
use = "VARS",
partition = dupPartition(data),
minclus = 1, \dots)
\method{as.hclust}{hc}(x, \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 (\eqn{n}) and
columns correspond to variables (\eqn{d}).
}
\item{modelName}{
A character string indicating the model to be used in model-based agglomerative hierarchical clustering.\cr
Possible models are:
\describe{
\item{\code{"E"}}{equal variance (one-dimensional);}
\item{\code{"V"}}{spherical, variable variance (one-dimensional);}
\item{\code{"EII"}}{spherical, equal volume;}
\item{\code{"VII"}}{spherical, unequal volume;}
\item{\code{"EEE"}}{ellipsoidal, equal volume, shape, and orientation;}
\item{\code{"VVV"}}{ellipsoidal, varying volume, shape, and orientation (default).}
}
If \code{hc()} is used for initialization of EM algorithm then the default is taken from \code{mclust.options("hcModelName")}. See \code{\link{mclust.options}}.
}
\item{use}{
A character string specifying the type of input variables/data transformation to be used for model-based agglomerative hierarchical clustering.\cr
Possible values are:
\describe{
\item{\code{"VARS"}}{original variables (default);}
\item{\code{"STD"}}{standardized variables (centered and scaled);}
\item{\code{"SPH"}}{sphered variables (centered, scaled and uncorrelated)
computed using SVD;}
\item{\code{"PCS"}}{principal components computed using SVD on centered
variables (i.e. using the covariance matrix);}
\item{\code{"PCR"}}{principal components computed using SVD on standardized
(center and scaled) variables (i.e. using the correlation matrix);}
\item{\code{"SVD"}}{scaled SVD transformation.}
}
If \code{hc()} is used for initialization of EM algorithm then the default is taken from \code{mclust.options("hcUse")}. See \code{\link{mclust.options}}.\cr
For further details see Scrucca and Raftery (2015).
}
\item{partition}{
A numeric or character vector representing a partition of
observations (rows) of \code{data}.
If provided, group merges will start with this partition.
Otherwise, each observation is assumed to be in a cluster by itself
at the start of agglomeration.
Starting with version 5.4.8, by default the function
\code{\link{dupPartition}} is used to start with all duplicated
observations in the same group, thereby keeping duplicates in the
same group throughout the modelling process.
}
\item{minclus}{
A number indicating the number of clusters at which to stop the
agglomeration. The default is to stop when all observations have been
merged into a single cluster.
}
\item{\dots}{
Arguments for the method-specific \code{hc} functions. See for example
\code{\link{hcE}}.
}
\item{x}{
An object of class \code{'hc'} resulting from a call to \code{hc()}.
}
}
\value{
The function \code{hc()} returns a numeric two-column matrix in which
the \emph{i}th row gives the minimum index for observations in each of
the two clusters merged at the \emph{i}th stage of agglomerative
hierarchical clustering. Several other informations are also returned
as attributes.
The method \code{as.hclust.hc()} can be used to convert the input
object from class \code{'hc'} to class \code{'hclust'}.
}
\details{
Most models have memory usage of the order of the square of the
number groups in the initial partition for fast execution.
Some models, such as equal variance or \code{"EEE"},
do not admit a fast algorithm under the usual agglomerative
hierarchical clustering paradigm.
These use less memory but are much slower to execute.
}
\note{
If \code{modelName = "E"} (univariate with equal variances) or
\code{modelName = "EII"} (multivariate with equal spherical
covariances), then underlying model is the same as that for
Ward's method for hierarchical clustering.
}
\references{
Banfield J. D. and Raftery A. E. (1993).
Model-based Gaussian and non-Gaussian Clustering.
\emph{Biometrics}, 49:803-821.
Fraley C. (1998).
Algorithms for model-based Gaussian hierarchical clustering.
\emph{SIAM Journal on Scientific Computing}, 20:270-281.
Fraley C. and Raftery A. E. (2002).
Model-based clustering, discriminant analysis, and density estimation.
\emph{Journal of the American Statistical Association}, 97:611-631.
Scrucca L. and Raftery A. E. (2015).
Improved initialisation of model-based clustering using Gaussian hierarchical partitions.
\emph{Advances in Data Analysis and Classification}, 9/4:447-460.
}
\seealso{
\code{\link{hcE}}, \dots,
\code{\link{hcVVV}},
\code{\link{plot.hc}},
\code{\link{hclass}},
\code{\link{mclust.options}}
}
\examples{
hcTree <- hc(modelName = "VVV", data = iris[,-5])
hcTree
cl <- hclass(hcTree,c(2,3))
table(cl[,"2"])
table(cl[,"3"])
\donttest{
clPairs(iris[,-5], classification = cl[,"2"])
clPairs(iris[,-5], classification = cl[,"3"])
}
}
\keyword{cluster}
|
