Mclust {mclust} | R Documentation

## Model-Based Clustering

### Description

Clustering via EM initialized by hierarchical clustering for parameterized Gaussian mixture models. The number of clusters and the clustering model is chosen to maximize the BIC.

### Usage

    Mclust(data, minG, maxG)

### 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.
`minG` | An integer vector specifying the minimum number of mixture components (clusters) to be considered. The default is `1` component.
`maxG` | An integer vector specifying the maximum number of mixture components (clusters) to be considered. The default is `9` components.

### Value

A list representing the best model (according to BIC) for the given range of numbers of clusters. The following components are included:

`BIC` | A matrix giving the BIC value for each model (rows) and number of clusters (columns).
`bic` | A scalar giving the optimal BIC value.
`modelName` | The MCLUST name for the best model according to BIC.
`classification` | The classification corresponding to the optimal BIC value.
`uncertainty` | The uncertainty in the classification corresponding to the optimal BIC value.
`mu` | For multidimensional models, a matrix whose columns are the means of each group in the best model. For one-dimensional models, a vector whose entries are the means for each group in the best model.
`sigma` | For multidimensional models, a three dimensional array in which `sigma[,,k]` gives the covariance for the kth group in the best model. 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` | The mixing probabilities for each component in the best model.
`z` | A matrix whose [i,k]th entry is the probability that observation i belongs to the k component in the model. The optimal classification is derived from this, chosing the class to be the one giving the maximum probability.
`loglik` | The log likelihood for the data under the best model.

### Details

The following models are compared in `Mclust`:
"E" for spherical, equal variance (one-dimensional)
"V" for spherical, variable variance (one-dimensional)
"EII": spherical, equal volume
"VII": spherical, unequal volume
"EEI": diagonal, equal volume, equal shape
"VVI": diagonal, varying volume, varying shape
"EEE": ellipsoidal, equal volume, shape, and orientation
"VVV": ellipsoidal, varying volume, shape, and orientation
`Mclust` is intended to combine `EMclust` and its `summary` in a simiplified one-step model-based clustering function. The latter provide more flexibility including choice of models.

### 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

`plot.Mclust`, `EMclust`

### Examples

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

    ## Not run: plot(irisMclust,irisMatrix)

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