EM algorithm starting with E-step for parameterized Gaussian mixture models

em {mclust}

R Documentation

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(modelName, data, parameters, prior = NULL, control = emControl(),
   warn = NULL, ...)

Arguments

modelName	A character string indicating the model. The help file for mclustModelNames describes the available models.
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.
parameters	A names list giving the parameters of the model. The components are as follows: 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. 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 kth component of the mixture model. variance A list of variance parameters for the model. The components of this list depend on the model specification. See the help file for mclustVariance for details. 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 hypvol to the data. Used only when pro includes an additional mixing proportion for a noise component.
prior	Specification of a conjugate prior on the means and variances. The default assumes no prior.
control	A list of control parameters for EM. The defaults are set by the call emControl().
warn	A logical value indicating whether or not a warning should be issued when computations fail. The default is warn=FALSE.
...	Catches unused arguments in indirect or list calls via do.call.

Value

A list including the following components:

modelName	A character string identifying the model (same as the input argument).
z	A matrix whose [i,k]th entry is the conditional probability of the ith observation belonging to the kth component of the mixture.
parameters	pro A vector whose kth component is the mixing proportion for the kth 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. 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 kth component of the mixture model. variance A list of variance parameters for the model. The components of this list depend on the model specification. See the help file for mclustVariance for details. 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.
loglik	The log likelihood for the data in the mixture model.
Attributes:	"info" Information on the iteration. "WARNING" An appropriate warning if problems are encountered in the computations.

References

C. Fraley and A. E. Raftery (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97:611-631.
C. Fraley and A. E. Raftery (2005). Bayesian regularization for normal mixture estimation and model-based clustering. Technical Report, Department of Statistics, University of Washington.
C. Fraley and A. E. Raftery (2006). MCLUST Version 3 for R: Normal Mixture Modeling and Model-Based Clustering, Technical Report no. 504, Department of Statistics, University of Washington.

See Also

emE, ..., emVVV, estep, me, mstep, mclustOptions, do.call

Examples

msEst <- mstep(modelName = "EEE", data = iris[,-5], 
               z = unmap(iris[,5]))
names(msEst)

em(modelName = msEst$modelName, data = iris[,-5],
   parameters = msEst$parameters)
## Not run: 
do.call("em", c(list(data = iris[,-5]), msEst))   ## alternative call
## End(Not run)

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[Package mclust version 3.1-1 Index]