K-Means clustering is known to be one of the simplest unsupervised learning algorithms that is capable of solving well known clustering problems.

K-Means clustering algorithm can be executed in order to solve a problem using four simple steps:

Make the partition of objects into K non empty steps i.e. K=1,2,3,.. .

Consider arbitrary seed points from sample data.

Calculate mean distance of sample data from seed points in order to generate clusters.

Repeat the above steps until values of two clusters becomes same. Below is an solved example.

Example : K-means Clustering

Criterion Function : Clustering

To measure the quality of clustering ability of any partitioned data set, criterion function is used.

Consider a set , B = { x_{1},x_{2},x_{3}…x_{n}} containing “n” samples, that is partitioned exactly into “t” disjoint subsets i.e. B_{1}, B_{2},…..,B_{t}.

The main highlight of these subsets is, every individual subset represents a cluster.

Sample inside the cluster will be similar to each other and dissimilar to samples in other clusters.

To make this possible, criterion functions are used according the occurred situations.

Criterion Function For Clustering

Internal Criterion Function

This class of clustering is an intra-cluster view.

Internal criterion function optimizes a function and measures the quality of clustering ability various clusters which are different from each other.

External Criterion Function

This class of clustering criterion is an inter-class view.

External Criterion Function optimizes a function and measures the quality of clustering ability of various clusters which are different from each other.

Hybrid Criterion Function

This function is used as it has the ability to simultaneously optimize multiple individual Criterion Functions unlike as Internal Criterion Function and External Criterion Function