Computes the prediction strength of clustering by
merging Gaussian mixture components, see `mergenormals`

.
The predictive strength is
defined according to Tibshirani and Walther (2005), carried out as
described in Hennig (2010), see details.

`mixpredictive(xdata, Gcomp, Gmix, M=50, ...)`

xdata

data (something that can be coerced into a matrix).

Gcomp

integer. Number of components of the underlying Gaussian mixture.

Gmix

integer. Number of clusters after merging Gaussian components.

M

integer. Number of times the dataset is divided into two halves.

...

further arguments that can potentially arrive in calls but are currently not used.

List with components

vector of length `M`

with relative frequencies of
correct predictions (clusterwise minimum).

mean of `predcorr`

.

The prediction strength for a certain number of clusters `Gmix`

under a
random partition of the dataset in halves A and B is defined as
follows. Both halves are clustered with `Gmix`

clusters. Then the points of
A are classified to the clusters of B. This is done by use of the
maximum a posteriori rule for mixtures as in Hennig (2010),
differently from Tibshirani and Walther (2005). A pair of points A in
the same A-cluster is defined to be correctly predicted if both points
are classified into the same cluster on B. The same is done with the
points of B relative to the clustering on A. The prediction strength
for each of the clusterings is the minimum (taken over all clusters)
relative frequency of correctly predicted pairs of points of that
cluster. The final mean prediction strength statistic is the mean over
all 2M clusterings.

Hennig, C. (2010) Methods for merging Gaussian mixture components,
*Advances in Data Analysis and Classification*, 4, 3-34.

Tibshirani, R. and Walther, G. (2005) Cluster Validation by
Prediction Strength, *Journal of Computational and Graphical
Statistics*, 14, 511-528.

`prediction.strength`

for Tibshirani and Walther's
original method.
`mergenormals`

for the clustering method applied here.

# NOT RUN { set.seed(98765) iriss <- iris[sample(150,20),-5] mp <- mixpredictive(iriss,2,2,M=2) # }