K Means clustering algorithm optimizes 2 objective functions at a time, minimizing the difference between elements within the cluster and maximizing the difference between clusters. So I want to understand which multi objective optimization technique is used in K Means?

# Which multi objective optimization technique is used by K-Means clustering? And can someone share some information about the optimization technique?

**tillutony**#2

Hi Ravi,

Description

Performs a multi-objective optimization for collecting cluster alternatives. The algorithm drawsR bootstrap samples from x. It calculates clusterings for all speciﬁed cluster numbers K using kmeans,neuralgas, and single-linkage clustering. It then applies several cluster validation indices to

the clusterings.

Usage

mocca(x, R = 50, K = 2:10, iter.max = 1000, nstart = 10)

Arguments

x 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 numeric columns).

R The number of bootstrap samples.

K The range of cluster numbers, i.e. a vector of integers listing the maximum

numbers of clusters to be used by each of the algorithms.

iter.max The maximum number of iterations allowed in k-means.

nstart For k-means, how many random sets should be chosen?

Value

A list with two entries:

cluster A list containing one sublist for each clustering algorithm and the baseline cluster

solution. Each of these lists hold an entry for each cluster size K, which

again consists of R vectors of cluster assignments. These vectors assign each

data point in x to a cluster.

objectiveVals A matrix of objective function values. Each row corresponds to a certain cluster

validation index applied to a certain clustering algorithm. The columns correspond

to different cluster numbers. Consequently, an entry of the matrix speciﬁes

the median value of a certain cluster validation index for a certain clustering

algorithm with a speciﬁc number of clusters over the R bootstrap samples.

Examples

data(toy5)

res <- mocca(toy5, R=10, K=2:5)

print(res$objectiveVals)

# plot kmeans result for MCA index against neuralgas result for MCA index

plot(res$objectiveVals[1,], res$objectiveVals[5,], pch=NA,

xlab=rownames(res$objectiveVals)[1], ylab=rownames(res$objectiveVals)[5])

text(res$objectiveVals[1,], res$objectiveVals[5,], labels=colnames(res$objectiveVals))

Regards,

tony