Prediction strength of merged Gaussian mixture
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. |
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.
List with components
predcorr |
vector of length |
mean.pred |
mean of |
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.
set.seed(98765) iriss <- iris[sample(150,20),-5] mp <- mixpredictive(iriss,2,2,M=2)
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