fpc (version 2.2-9)

mixpredictive: Prediction strength of merged Gaussian mixture

Description

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.

Usage

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

Arguments

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.

Value

List with components

predcorr

vector of length `M` with relative frequencies of correct predictions (clusterwise minimum).

mean.pred

mean of `predcorr`.

Details

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.

References

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.
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