fpc (version 2.1-6)

prediction.strength: Prediction strength for estimating number of clusters

Description

Computes the prediction strength of a clustering of a dataset into different numbers of components. The prediction strength is defined according to Tibshirani and Walther (2005), who recommend to choose as optimal number of cluster the largest number of clusters that leads to a prediction strength above 0.8 or 0.9. See details.

Various clustering methods can be used, see argument clustermethod.

Usage

prediction.strength(xdata, Gmin=2, Gmax=10, M=50,
                      clustermethod=kmeansCBI,
                                classification="centroid",
                                cutoff=0.8,nnk=1,
                      distances=inherits(xdata,"dist"),count=FALSE,...)
  ## S3 method for class 'predstr':
print(x, ...)

Arguments

xdata

data (something that can be coerced into a matrix). Note that this can currently not be a dissimilarity matrix.

Gmin

integer. Minimum number of clusters. Note that the prediction strength for 1 cluster is trivially 1, which is automatically included if GMin>1. Therefore GMin<2< code=""> is useless.

Gmax

integer. Maximum number of clusters.

M

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

clustermethod

an interface function (the function name, not a string containing the name, has to be provided!). This defines the clustering method. See the "Details"-section of clusterboot and

classification

string. This determines how non-clustered points are classified to given clusters. Options are explained in classifnp. Certain classification methods are connected to certain clustering me

cutoff

numeric between 0 and 1. The optimal number of clusters is the maximum one with prediction strength above cutoff.

nnk

number of nearest neighbours if classification="knn", see classifnp.

distances

logical. If TRUE, data will be interpreted as dissimilarity matrix, passed on to clustering methods as "dist"-object, and classifdist will be used for classificatio

count

logical. TRUE will print current number of clusters and simulation run number on the screen.

x

object of class predstr.

...

arguments to be passed on to the clustering method.

Value

• prediction.strength gives out an object of class predstr, which is a list with components
• predcorr
  list of vectors of length M with relative frequencies of correct predictions (clusterwise minimum). Every list entry refers to a certain number of clusters.
• mean.pred
  means of predcorr for all numbers of clusters.
• optimalk
  optimal number of clusters.
• cutoff
  see above.
• method
  a string identifying the clustering method.
• Gmax
  see above.
• M
  see above.

Details

The prediction strength for a certain number of clusters k under a random partition of the dataset in halves A and B is defined as follows. Both halves are clustered with k clusters. Then the points of A are classified to the clusters of B. In the original paper this is done by assigning every observation in A to the closest cluster centroid in B (corresponding to classification="centroid"), but other methods are possible, see classifnp. 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

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

See Also

kmeansCBI, classifnp

Examples

set.seed(98765)
  iriss <- iris[sample(150,20),-5]
  prediction.strength(iriss,2,3,M=3)
  prediction.strength(iriss,2,3,M=3,clustermethod=claraCBI)
# The examples are fast, but of course M should really be larger.