ICL (Integrated Complete-data Likelihood) for parameterized Gaussian mixture models fitted by EM algorithm initialized by model-based hierarchical clustering.

```
mclustICL(data, G = NULL, modelNames = NULL,
initialization = list(hcPairs = NULL,
subset = NULL,
noise = NULL),
x = NULL, ...)
```# S3 method for mclustICL
summary(object, G, modelNames, ...)

Returns an object of class `'mclustICL'`

containing the the ICL criterion
for the specified mixture models and numbers of clusters.

The corresponding `print`

method shows the matrix of values and the top models according to the ICL criterion. The `summary`

method shows only the top models.

- 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.

- G
An integer vector specifying the numbers of mixture components (clusters) for which the criteria should be calculated. The default is

`G = 1:9`

.- modelNames
A vector of character strings indicating the models to be fitted in the EM phase of clustering. The help file for

`mclustModelNames`

describes the available models. The default is:`c("E", "V")`

for univariate data

`mclust.options("emModelNames")`

for multivariate data (n > d)

`c("EII", "VII", "EEI", "EVI", "VEI", "VVI")`

the spherical and diagonal models for multivariate data (n <= d)

A list containing zero or more of the following components:

`hcPairs`

A matrix of merge pairs for hierarchical clustering such as produced by function

`hc`

. For multivariate data, the default is to compute a hierarchical clustering tree by applying function`hc`

with`modelName = "VVV"`

to the data or a subset as indicated by the`subset`

argument. The hierarchical clustering results are to start EM. For univariate data, the default is to use quantiles to start EM.

`subset`

A logical or numeric vector specifying a subset of the data to be used in the initial hierarchical clustering phase.

An object of class `'mclustICL'`

. If supplied, `mclustICL`

will use the settings in `x`

to produce another object of
class `'mclustICL'`

, but with `G`

and `modelNames`

as specified in the arguments. Models that have already been computed
in `x`

are not recomputed. All arguments to `mclustICL`

except `data`

, `G`

and `modelName`

are
ignored and their values are set as specified in the attributes of
`x`

.
Defaults for `G`

and `modelNames`

are taken from `x`

.

Futher arguments used in the call to `Mclust`

.
See also `mclustBIC`

.

An integer vector specifying the numbers of mixture components
(clusters) for which the criteria should be calculated.
The default is `G = 1:9`

.

Biernacki, C., Celeux, G., Govaert, G. (2000).
Assessing a mixture model for clustering with the integrated completed likelihood.
*IEEE Trans. Pattern Analysis and Machine Intelligence*, 22 (7), 719-725.

Scrucca L., Fop M., Murphy T. B. and Raftery A. E. (2016) mclust 5: clustering, classification and density estimation using Gaussian finite mixture models, *The R Journal*, 8/1, pp. 289-317.

`plot.mclustICL`

,
`Mclust`

,
`mclustBIC`

,
`mclustBootstrapLRT`

,
`bic`

,
`icl`

```
data(faithful)
faithful.ICL <- mclustICL(faithful)
faithful.ICL
summary(faithful.ICL)
plot(faithful.ICL)
# \donttest{
# compare with
faithful.BIC <- mclustBIC(faithful)
faithful.BIC
plot(faithful.BIC)
# }
```

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