mclust (version 5.2.2)

MclustDR: Dimension reduction for model-based clustering and classification

Description

A dimension reduction method for visualizing the clustering or classification structure obtained from a finite mixture of Gaussian densities.

Usage

MclustDR(object, normalized = TRUE, Sigma, lambda = 0.5,  tol = sqrt(.Machine$double.eps))

Arguments

object

An object of class 'Mclust' or 'MclustDA' resulting from a call to, respectively, Mclust or MclustDA.

normalized

Logical. If TRUE directions are normalized to unit norm.

Sigma

Marginal covariance matrix of data. If not provided is estimated by the MLE of observed data.

lambda

A tuning parameter in the range [0,1] described in Scrucca (2014). The default 0.5 gives equal importance to differences in means and covariances among clusters/classes. To recover the directions that mostly separate the estimated clusters or classes set this parameter to 1.

tol

A tolerance value.

Value

An object of class 'MclustDR' with the following components:

Details

The method aims at reducing the dimensionality by identifying a set of linear combinations, ordered by importance as quantified by the associated eigenvalues, of the original features which capture most of the clustering or classification structure contained in the data.

Information on the dimension reduction subspace is obtained from the variation on group means and, depending on the estimated mixture model, on the variation on group covariances (see Scrucca, 2010).

Observations may then be projected onto such a reduced subspace, thus providing summary plots which help to visualize the underlying structure.

The method has been extended to the supervised case, i.e. when the true classification is known (see Scrucca, 2013).

This implementation doesn't provide a formal procedure for the selection of dimensionality. A future release will include one or more methods.

References

Scrucca, L. (2010) Dimension reduction for model-based clustering. Statistics and Computing, 20(4), pp. 471-484.

C. Fraley, A. E. Raftery, T. B. Murphy and L. Scrucca (2012). mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report No. 597, Department of Statistics, University of Washington.

Scrucca, L. (2014) Graphical Tools for Model-based Mixture Discriminant Analysis. Advances in Data Analysis and Classification, 8(2), pp. 147-165

See Also

summary.MclustDR, plot.MclustDR, Mclust, MclustDA.

Examples

# clustering
data(diabetes)
mod = Mclust(diabetes[,-1])
summary(mod)

dr = MclustDR(mod)
summary(dr)
plot(dr, what = "scatterplot")
plot(dr, what = "evalues")

# adjust the tuning parameter to show the most separating directions
dr1 = MclustDR(mod, lambda = 1) 
summary(dr1)
plot(dr1, what = "scatterplot")
plot(dr1, what = "evalues")

# classification
data(banknote)

da = MclustDA(banknote[,2:7], banknote$Status, modelType = "EDDA")
dr = MclustDR(da)
summary(dr)

da = MclustDA(banknote[,2:7], banknote$Status)
dr = MclustDR(da)
summary(dr)