meE {mclust} | R Documentation

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

### Description

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

### Usage

    meE(data, z, eps, tol, itmax, equalPro, warnSingular,
        noise = FALSE, Vinv)
    meV(data, z, eps, tol, itmax, equalPro, warnSingular,
        noise = FALSE, Vinv)
    meEII(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)
    meVII(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)
    meEEI(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)
    meVEI(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)
    meEVI(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)
    meVVI(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)
    meEEE(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)
    meEEV(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)
    meVEV(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)
    meVVV(data, z, eps, tol, itmax, equalPro, warnSingular,
          noise = FALSE, Vinv)

### Arguments

`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.
`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`.
`tol` | A scalar tolerance for relative convergence of the loglikelihood values. The default is `.Mclust\$tol`.
`itmax` | An integer limit on the number of EM iterations. The default is `.Mclust\$itmax`.
`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.
`modelName` | Character string identifying the model.
`loglik` | The logliklihood for the data in the mixture model.
`Attributes:` | The return value also has the following 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

`em`, `me`, `estep`, `mclustOptions`

### Examples

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

    meVVV(data = irisMatrix, z = unmap(irisClass))

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