mclust (version 1.1-7)

mhtree.VVV: Classification tree for hierarchical clustering for Gaussian models with unconstrained variance.

Description

Computes a classification tree for agglomerative hierarchical clustering using a Gaussian model in which volume, shape, and orientation may vary among clusters.

Usage

mhtree.VVV(data, partition, min.clusters = 1, alpha = 1, beta = 1)

Arguments

data

matrix of observations.

partition

initial classification of the data. The default puts every observation in a singleton cluster.

min.clusters

minimum number of clusters desired. The default is to carry out agglomerative hierarchical clustering until termination, that is, until all observations belong to a single group. The default value is 1.

alpha

The value alpha times the trace of the sample crossproduct matrix of all the observations divided by the product of the data dimensions, is used for the purpose of initalization. The default value is 1.

beta

The value beta times the trace of the sample crossproduct matrix for the group divided by the number of observations in the group, is used for the purpose of initialization. The default value is 1.

Value

• an object of class "mhtree", which consists of a classification tree with the following attributes:
• call
  a copy of the call to mhtree.VVV.
• change
  value of the optimal change in likelihood at each stage.
• dimensions
  the data dimensions.
• initial.partition
  the partition at which agglomerative hierarchical clustering is initiated.

NOTES

The values alpha and beta are needed since the criteria are not defined for groups for which the rank of the sample cross product matrix is less than the dimension of the observations.

References

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

C. Fraley, Algorithms for Model-based Gaussian Hierarchical Clustering,Technical Report No. 311, Department of Statistics, University of Washington (October 1996), to appear in SIAM Journal on Scientific Computing.

A. J. Scott and M. J. Simons, Clustering methods based on likelihood ratio criteria, Biometrics,27:387-397 (1971).

See Also

mhtree, mhclass, awe, partuniq

Examples

data(iris)
mhtree.VVV(iris[,1:4])