# pamk

0th

Percentile

##### Partitioning around medoids with estimation of number of clusters

This calls the function pam or clara to perform a partitioning around medoids clustering with the number of clusters estimated by optimum average silhouette width (see pam.object) or Calinski-Harabasz index (calinhara). 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 or data are dissimilarities).

Keywords
multivariate, cluster
##### Usage
pamk(data,krange=2:10,criterion="asw", usepam=TRUE, scaling=FALSE, alpha=0.001, diss=inherits(data, "dist"), critout=FALSE, ns=10, seed=NULL, ...)
##### Arguments
data
a data matrix or data frame or something that can be coerced into a matrix, or dissimilarity matrix or object. See pam for more information.
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", "multiasw" or "ch". Determines whether average silhouette width (as given out by pam/clara, or as computed by distcritmulti if "multiasw" is specified; recommended for large data sets with usepam=FALSE) or Calinski-Harabasz is applied. Note that the original Calinski-Harabasz index is not defined for dissimilarities; if dissimilarity data is run with criterion="ch", the dissimilarity-based generalisation in Hennig and Liao (2013) is used.
usepam
logical. If TRUE, pam is used, otherwise clara (recommended for large datasets with 2,000 or more observations; dissimilarity matrices can not be used with clara).
scaling
either a logical value or a numeric vector of length equal to the number of variables. If scaling is a numeric vector with length equal to the number of variables, then each variable is divided by the corresponding value from scaling. If scaling is TRUE then scaling is done by dividing the (centered) variables by their root-mean-square, and if scaling is FALSE, no scaling is done.
alpha
numeric between 0 and 1, tuning constant for dudahart2 (only used for 1-cluster test).
diss
logical flag: if TRUE (default for dist or dissimilarity-objects), then data will be considered as a dissimilarity matrix (and the potential number of clusters 1 will be ignored). If FALSE, then data will be considered as a matrix of observations by variables.
critout
logical. If TRUE, the criterion value is printed out for every number of clusters.
ns
passed on to distcritmulti if criterion="multiasw".
seed
passed on to distcritmulti if criterion="multiasw".
...
further arguments to be transferred to pam or clara.
##### Value

A list with components
pamobject
The output of the optimal run of the pam-function.
nc
the optimal number of clusters.
crit
vector of criterion values for numbers of clusters. crit[1] is the p-value of the Duda-Hart test if 1 is in krange and diss=FALSE.

##### Note

clara and pam can handle NA-entries (see their documentation) but dudahart2 cannot. Therefore NA should not occur if 1 is in krange.

##### References

Calinski, R. B., 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.

Hennig, C. and Liao, T. (2013) How to find an appropriate clustering for mixed-type variables with application to socio-economic stratification, Journal of the Royal Statistical Society, Series C Applied Statistics, 62, 309-369.

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

pam, clara distcritmulti

• pamk
##### Examples
  options(digits=3)
set.seed(20000)
face <- rFace(50,dMoNo=2,dNoEy=0,p=2)
pk1 <- pamk(face,krange=1:5,criterion="asw",critout=TRUE)
pk2 <- pamk(face,krange=1:5,criterion="multiasw",ns=2,critout=TRUE)
# "multiasw" is better for larger data sets, use larger ns then.
pk3 <- pamk(face,krange=1:5,criterion="ch",critout=TRUE)

Documentation reproduced from package fpc, version 2.1-10, License: GPL

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