clusterSim (version 0.51-5)

initial.Centers: Calculation of initial clusters centers for k-means like alghoritms

Description

Function calculates initial clusters centers for k-means like alghoritms with the following alghoritm (similar to SPSS QuickCluster function)

(a) if the distance between \(x_k\) and its closest cluster center is greater than the distance between the two closest centers (\(M_m\) and \(M_n\) ), then \(x_k\) replaces either \(M_m\) or \(M_n\), whichever is closer to \(x_k\).

(b) If \(x_k\) does not replace a cluster initial center in (a), a second test is made: If that distance \(d_q\) greater than the distance between \(M_q\) and its closest \(M_i\), then \(x_k\) replaces \(M_q\).

where:

\(M_i\) - initial center of i-th cluster

\(x_k\) - vector of k-th observation

\(d(...,...)\) - Euclidean distance

\(d_{mn}\) = \(min_{ij} d(M_i,M_j)\)

\(d_q = min_i d(x_k,M_i)\)

Usage

initial.Centers(x, k)

Value

Numbers of objects choosen as initial cluster centers

Arguments

x

matrix or dataset

k

number of initial cluster centers

Author

Marek Walesiak , Andrzej Dudek

Department of Econometrics and Computer Science, University of Economics, Wroclaw, Poland

References

Hartigan, J. (1975), Clustering algorithms, Wiley, New York. ISBN 0-471-35645-X.

See Also

cluster.Sim

Examples

#Example 1 (numbers of objects choosen as initial cluster centers)
library(clusterSim)
data(data_ratio)
ic <- initial.Centers(data_ratio, 10)
print(ic)

#Example 2 (application with kmeans algorithm)
library(clusterSim)
data(data_ratio)
kmeans(data_ratio,data_ratio[initial.Centers(data_ratio, 10),])