nClust {anocva}

Optimal Number of Clusters Estimation

Description

Estimates the optimal number of clusters using either Slope or Silhouette criterion. The optimal number of clusters will be verified in the range 2,..., maxClust.

Usage

nClust(meanDist, p = 1, maxClust = 20, clusteringFunction,
  criterion = c("slope", "silhouette"))

Arguments

meanDist

An NxN matrix that represents the distances between the N items of the sample.

p

Slope adjust parameter.

maxClust

The maximum number of clusters to be tried. The default value is 20.

clusteringFunction

The clustering function to be used.

criterion

The criterion that will be used for estimating the number of clusters. The options are "slope" or "silhouette". If not defined, "slope" will be used.

Value

The optimal number of clusters.

References

Fujita A, Takahashi DY, Patriota AG (2014b) A non-parametric method to estimate the number of clusters. Computational Statistics & Data Analysis 73:27–39

Rousseeuw PJ (1987) Sihouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics 20:53–65

Examples

# Install packages if necessary
# install.packages('MASS')
# install.packages('cluster')

library(MASS)
library(cluster)
library(anocva)

set.seed(2000)

# Defines a k-means function that returns cluster labels directly
myKmeans = function(dist, k){
  return(kmeans(dist, k, iter.max = 50, nstart = 5)$cluster)
}

# Generate simulated data
nitem = 70
sigma = matrix(c(0.04, 0, 0, 0.04), 2)
simuData = rbind(mvrnorm(nitem, mu = c(0, 0), Sigma = sigma ),
             mvrnorm(nitem, mu = c(3,0), Sigma = sigma),
             mvrnorm(nitem, mu = c(2.5,2), Sigma = sigma))

plot(simuData, asp = 1, xlab = '', ylab = '', main = 'Data for clustering')

# Calculate distances and perform {0,1} normalization
distMatrix = as.matrix(dist(simuData))
distMatrix = checkRange01(distMatrix)

# Estimate the optimal number of clusters
r = nClust(meanDist = distMatrix, p = 1, maxClust = 10,
           clusteringFunction = myKmeans, criterion = "silhouette")
sprintf("The optimal number of clusters found was %d.", r)

# K-means Clustering
labels = myKmeans(distMatrix, r)

plot(simuData, col = labels, asp = 1, xlab = '', ylab = '', main = 'K-means clustered data')