# CLUSTER ANALYSIS

Cluster analysis is a process in which the individuals or objects are corresponding but are distinct to the groups of other corresponding individuals or objects. For example you can cluster those children in the class who are undisciplined, who are intelligent or who are naughty.

## METHODS OF CLUSTER ANALYSIS

There are three methods of cluster analysis

Hierarchical cluster analysis

K – means cluster

Two step cluster analysis

Hierarchical cluster analysis – it is one of the most straightforward method. If you have a small set of statics data and you want to examine the results in an easy way, then this method is used. The two methods of hierarchical cluster analysis are agglomerative and divisive. In agglomerative method the procedure starts with single elements and then aggregates into cluster. In divisive method, the procedure starts with one set of data and ends with the partition of the various clusters. In agglomerative, once a cluster is formed then it cannot split and join into another cluster whereas the whole cluster will join the other cluster.

To form cluster one must require –

A criterion for evaluating distance or similarity between cases.

A criterion to evaluate that at which step what sort of clusters is required.

The requirement of the number of clusters for the representation of data.For example there are a group of judges who want to take out the best 10 contestants among the 20 for Ms. India. They judge the contestants on the basis of the given scale. You have to analyse which are the best 10, so you will judge with the help of the highest, second highest, third highest and so on and if a tie is there then you group those contestants in a cluster where they have to clear tie test but without it they can’t join the contestants.

K – Means cluster–The method which does not requires computation of all the distances is done by k – means clustering. In this clustering you have to know the number of clusters to be formed in advance. The algorithm is called k – means where k is the number of clusters for which the distance to the cluster mean is the smallest. For example if you want the excavations of any antique object belonging to the age of early man, then you will analyse the object through size, colour, texture, and the time period of the object. You can also use the latest technology to take out the excavation. So you will perform the clusters of metals in the object, colours and so on with their mean.
Two step clusters – In this process you need to categorise a large set of data into two basic sets having different categories. It is based on the measurement of distances which have independent and continuous variables with normal distribution.

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