me {mclust} | R Documentation

## EM algorithm starting with M-step for parameterized MVN mixture models.

### Description

Implements the EM algorithm for parameterized MVN mixture models, starting with the maximization step.

### Usage

    me(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: 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`. For those models with iterative M-step ("VEI", "VEV"), two values can be entered for `eps`, in which case the second value is used for determining singularity in the M-step. tol A scalar tolerance for relative convergence of the loglikelihood. The default is `.Mclust\$tol`. For those models with iterative M-step ("VEI", "VEV"), two values can be entered for `tol`, in which case the second value governs parameter convergence in the M-step. itmax An integer limit on the number of EM iterations. The default is `.Mclust\$itmax`. For those models with iterative M-step ("VEI", "VEV"), two values can be entered for `itmax`, in which case the second value is an upper limit on the number of iterations in the M-step. equalPro Logical variable indicating whether or not the mixing proportions are equal in the model. The default is `.Mclust\$equalPro`. warnSingular A logical value indicating whether or not a warning should be issued whenever a singularity is encountered. The default is `.Mclust\$warnSingular`. noise A logical value indicating whether or not the model includes a Poisson noise component. The default assumes there is no noise component. 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 `noise = TRUE`.

### 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.
`loglik` | The logliklihood for the data in the mixture model.
`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

`meE`,..., `meVVV`, `em`, `mstep`, `estep`, `mclustOptions`

### Examples

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

    me(modelName = "VVV", data = irisMatrix, z = unmap(irisClass))

[Package Contents]