Agglomerative hierarchical clustering based on maximum likelihood criteria for Gaussian mixture models parameterized by eigenvalue decomposition.

hc(data,
modelName = mclust.options("hcModelName"),
partition, minclus = 1, ...,
use = mclust.options("hcUse"))

## 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 ($$n$$) and columns correspond to variables ($$d$$). A character string indicating the model to be used. Possible models are: "E"equal variance (one-dimensional) "V"spherical, variable variance (one-dimensional) "EII"spherical, equal volume "VII"spherical, unequal volume "EEE"ellipsoidal, equal volume, shape, and orientation "VVV"ellipsoidal, varying volume, shape, and orientation. By default the model provided by mclust.options("hcModelName") is used. See mclust.options. A numeric or character vector representing a partition of observations (rows) of data. If provided, group merges will start with this partition. Otherwise, each observation is assumed to be in a cluster by itself at the start of agglomeration. A number indicating the number of clusters at which to stop the agglomeration. The default is to stop when all observations have been merged into a single cluster. Arguments for the method-specific hc functions. See for example hcE. A string or a vector of character strings specifying the type of input variables/data transformation to be used for model-based hierarchical clustering. By default the method specified in mclust.options("hcUse") is used. See mclust.options.

## Value

The function hc() returns a numeric two-column matrix in which the ith row gives the minimum index for observations in each of the two clusters merged at the ith stage of agglomerative hierarchical clustering. Several other informations are also returned as attributes.

The plotting method plot.hc() draws a dendrogram, which can be based on either the classification loglikelihood or the merge level (number of clusters). For details, see the associated help file.

## Details

Most models have memory usage of the order of the square of the number groups in the initial partition for fast execution. Some models, such as equal variance or "EEE", do not admit a fast algorithm under the usual agglomerative hierarchical clustering paradigm. These use less memory but are much slower to execute.

## Note

If modelName = "E" (univariate with equal variances) or modelName = "EII" (multivariate with equal spherical covariances), then underlying model is the same as that for Ward's method for hierarchical clustering.

## References

J. D. Banfield and A. E. Raftery (1993). Model-based Gaussian and non-Gaussian Clustering. Biometrics 49:803-821.

C. Fraley (1998). Algorithms for model-based Gaussian hierarchical clustering. SIAM Journal on Scientific Computing 20:270-281.

C. Fraley and A. E. Raftery (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97:611-631.

hcE, ..., hcVVV, plot.hc, hclass, mclust.options

## Examples

hcTree <- hc(modelName = "VVV", data = iris[,-5])
hcTree
#> Call:
#> hc(data = iris[, -5], modelName = "VVV")
#>
#> Model-Based Agglomerative Hierarchical Clustering
#> Model name        = VVV
#> Use               = SVD
#> Number of objects = 150 cl <- hclass(hcTree,c(2,3))
table(cl[,"2"])
#>
#>   1   2
#>  49 101 table(cl[,"3"])
#>
#>  1  2  3
#> 49 62 39
if (FALSE) {
clPairs(iris[,-5], classification = cl[,"2"])
clPairs(iris[,-5], classification = cl[,"3"])
}