kmeansruns {fpc}

k-means with estimating k and initialisations

Description

This calls the function kmeans to perform a k-means clustering, but initializes the k-means algorithm several times with random points from the data set as means. Furthermore, it is more robust against the occurrence of empty clusters in the algorithm and it estimates the number of clusters by either the Calinski Harabasz index (calinhara) or average silhouette width (see pam.object). The Duda-Hart test (dudahart2) is applied to decide whether there should be more than one cluster (unless 1 is excluded as number of clusters).

Usage

kmeansruns(data,krange=2:10,criterion="ch",
                       iter.max=100,runs=100,
                       scaledata=FALSE,alpha=0.001,
                       critout=FALSE,plot=FALSE,...)

Arguments

data

A numeric matrix of data, or an object that can be coerced to such a matrix (such as a numeric vector or a data frame with all numeric columns).

krange

integer vector. Numbers of clusters which are to be compared by the average silhouette width criterion. Note: average silhouette width and Calinski-Harabasz can't estimate number of clusters nc=1. If 1 is included, a Duda-Hart test is applied and 1 is estimated if this is not significant.

criterion

one of "asw" or "ch". Determines whether average silhouette width or Calinski-Harabasz is applied.

iter.max

integer. The maximum number of iterations allowed.

runs

integer. Number of starts of the k-means algorithm.

scaledata

logical. If TRUE, the variables are centered and scaled to unit variance before execution.

alpha

numeric between 0 and 1, tuning constant for dudahart2 (only used for 1-cluster test).

critout

logical. If TRUE, the criterion value is printed out for every number of clusters.

plot

logical. If TRUE, every clustering resulting from a run of the algorithm is plotted.

...

further arguments to be passed on to kmeans.

Value

The output of the optimal run of the kmeans-function with added components bestk and crit. A list with components

cluster

A vector of integers indicating the cluster to which each point is allocated.

centers

A matrix of cluster centers.

withinss

The within-cluster sum of squares for each cluster.

size

The number of points in each cluster.

bestk

The optimal number of clusters.

crit

Vector with values of the criterion for all used numbers of clusters (0 if number not tried).

Author(s)

Christian Hennig [e-mail] https://www.unibo.it/sitoweb/christian.hennig/en/

References

Calinski, T., and Harabasz, J. (1974) A Dendrite Method for Cluster Analysis, Communications in Statistics, 3, 1-27.

Duda, R. O. and Hart, P. E. (1973) Pattern Classification and Scene Analysis. Wiley, New York.

Hartigan, J. A. and Wong, M. A. (1979). A K-means clustering algorithm. Applied Statistics, 28, 100-108.

Kaufman, L. and Rousseeuw, P.J. (1990). "Finding Groups in Data: An Introduction to Cluster Analysis". Wiley, New York.

See Also

kmeans, pamk, calinhara, dudahart2)

Examples

  options(digits=3)
  set.seed(20000)
  face <- rFace(50,dMoNo=2,dNoEy=0,p=2)
  pka <- kmeansruns(face,krange=1:5,critout=TRUE,runs=2,criterion="asw")
  pkc <- kmeansruns(face,krange=1:5,critout=TRUE,runs=2,criterion="ch")