R: Prediction strength for estimating number of clusters

prediction.strength {fpc} | R Documentation

## 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` 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 `kmeansCBI` for the format. Clustering methods for `prediction.strength` must have a `k`-argument for the number of clusters, must operate on n times p data matrices and must otherwise follow the specifications in `clusterboot`.
`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 methods. `classification="averagedist"` is recommended for average linkage, `classification="centroid"` is recommended for k-means, clara and pam, `classification="knn"` with `nnk=1` is recommended for single linkage and `classification="qda"` is recommended for Gaussian mixtures with flexible covariance matrices.
`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 classification.
`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.

### 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.

### 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.

### Author(s)

Christian Hennig c.hennig@ucl.ac.uk http://www.homepages.ucl.ac.uk/~ucakche/

### 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

      options(digits=3)
      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.

[Package fpc version 2.1-10 Index]