R: EM algorithm starting with E-step for parameterized Gaussian...

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).
`n`	The number of observations in the data.
`d`	The dimension of the data.
`G`	The number of mixture components.
`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.
`control`	The list of control parameters for EM used.
`prior`	The specification of a conjugate prior on the means and variances used, `NULL` if no prior is used.
`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 (2007). Bayesian regularization for normal mixture estimation and model-based clustering. Journal of Classification 24:155-181.

C. Fraley, A. E. Raftery, T. B. Murphy and L. Scrucca (2012). mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report No. 597, Department of Statistics, University of Washington.

Examples

## Not run: 
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

## End(Not run)

[Package mclust version 5.3 Index]