mstep {mclust}R Documentation

M-step in the EM algorithm for parameterized MVN mixture models.

Description

Maximization step in the EM algorithm for parameterized MVN mixture models.

Usage

mstep(modelName, data, z, ...)

Arguments

modelName A character string indicating the model:

"E": equal variance (one-dimensional)
"V": variable variance (one-dimensional)
"EII": spherical, equal volume
"VII": spherical, unequal volume
"EEI": diagonal, equal volume and shape
"VEI": diagonal, varying volume, equal shape
"EVI": diagonal, equal volume, varying shape
"VVI": diagonal, varying volume and shape
"EEE": ellipsoidal, equal volume, shape, and orientation
"EEV": ellipsoidal, equal volume and equal shape
"VEV": ellipsoidal, equal shape
"VVV": ellipsoidal, varying volume, shape, and orientation
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.
z A matrix whose [i,k]th entry is the conditional probability of the ith observation belonging to the kth component of the mixture.
... Any number of the following:
equalPro
A logical value indicating whether or not the components in the model are present in equal proportions. The default is .Mclust\$equalPro.
noise
A logical value indicating whether or not the model includes a Poisson noise component. The default assumes there is no noise component.
eps
A scalar tolerance for deciding when to terminate computations due to computational singularity in covariances. Smaller values of eps allows computations to proceed nearer to singularity. The default is .Mclust\$eps.
Not used for models "EII", "VII", "EEE", "VVV".
tol
For models with iterative M-step ("VEI", "VEE", "VVE", "VEV"), a scalar tolerance for relative convergence of the parameters. The default is .Mclust\$tol.
itmax
For models with iterative M-step ("VEI", "VEE", "VVE", "VEV"), an integer limit on the number of EM iterations. The default is .Mclust\$itmax.
warnSingular
A logical value indicating whether or not a warning should be issued whenever a singularity is encountered. The default is .Mclust\$warnSingular.
Not used for models "EII", "VII", "EEE", "VVV".

Value

A list including the following components:

mu A matrix whose kth column is the mean of the kth component of the mixture model.
sigma For multidimensional models, a three dimensional array in which the [,,k]th entry gives the the covariance for the kth group in the best model. <br> For one-dimensional models, either a scalar giving a common variance for the groups or a vector whose entries are the variances for each group in the best model.
pro A vector whose kth component is the mixing proportion for the kth component of the mixture model.
z A matrix whose [i,k]th entry is the conditional probability of the ith observation belonging to the kth component of the mixture.
modelName A character string identifying the model (same as the input argument).
Attributes:
  • "info": Information on the iteration.
  • "warn": An appropriate warning if problems are encountered in the computations.
  • References

    C. Fraley and A. E. Raftery (2002a). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97:611-631. See http://www.stat.washington.edu/mclust.

    C. Fraley and A. E. Raftery (2002b). MCLUST:Software for model-based clustering, density estimation and discriminant analysis. Technical Report, Department of Statistics, University of Washington. See http://www.stat.washington.edu/mclust.

    See Also

    mstepE, ..., mstepVVV, me, estep, mclustOptions.

    Examples

    data(iris)
    irisMatrix <- as.matrix(iris[,1:4])
    irisClass <- iris[,5]
     
    mstep(modelName = "VII", data = irisMatrix, z = unmap(irisClass))
    

    [Package mclust version 2.1-11 Index]