estep {mclust}R Documentation

E-step for parameterized MVN mixture models.

Description

Implements the expectation step of EM algorithm for parameterized MVN mixture models.

Usage

estep(modelName, data, mu, ...)

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.
mu The mean for each component. If there is more than one component, mu is a matrix whose columns are the means of the components.
... Arguments for model-specific functions. Specifically:
  • An argument describing the variance (depends on the model):
    sigmasq
    for the one-dimensional models ("E", "V") and spherical models ("EII", "VII"). This is either a vector whose kth component is the variance for the kth component in the mixture model ("V" and "VII"), or a scalar giving the common variance for all components in the mixture model ("E" and "EII").
    decomp
    for the diagonal models ("EEI", "VEI", "EVI", "VVI") and some ellipsoidal models ("EEV", "VEV"). This is a list described in cdens.
    Sigma
    for the equal variance model "EEE". A d by d matrix giving the common covariance for all components of the mixture model.
    sigma
    for the unconstrained variance model "VVV". A d by d by G matrix array whose [,,k]th entry is the covariance matrix for the kth component of the mixture model.
    The form of the variance specification is the same as for the output for the em, me, or mstep methods for the specified mixture model.
    pro
    Mixing proportions for the components of the mixture. There should one more mixing proportion than the number of MVN components if the mixture model includes a Poisson noise term.
    eps
    A scalar tolerance for deciding when to terminate computations due to computational singularity in covariances. Smaller values of eps allow computations to proceed nearer to singularity. The default is .Mclust\$eps.
    warnSingular
    A logical value indicating whether or not a warning should be issued whenever a singularity is encountered. The default is .Mclust\$warnSingular.
    Vinv
    An estimate of the reciprocal hypervolume of the data region. The default is determined by applying function hypvol to the data. Used only when pro includes an additional mixing proportion for a noise component.

Details

This function can be used with an indirect or list call using do.call, allowing the output of e.g. mstep to be passed without the need to specify individual parameters as arguments.

Value

A list including the following 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.
loglik The logliklihood for the data in the mixture model.
modelName A character string identifying the model (same as the input argument).
Attribute
  • "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

estepE, ..., estepVVV, em, mstep, do.call, mclustOptions

Examples

data(iris)
irisMatrix <- as.matrix(iris[,1:4])
irisClass <- iris[,5]

msEst <- mstep(modelName = "EII", data = irisMatrix, 
               z = unmap(irisClass))
names(msEst)

estep(modelName = msEst$modelName, data = irisMatrix,
      mu = msEst$mu, sigmasq = msEst$sigmasq, pro = msEst$pro)           
## Not run: 
do.call("estep", c(list(data = irisMatrix), msEst))   ## alternative call
## End(Not run)

[Package mclust version 2.1-11 Index]