CLUSTER ANALYSIS by vaibhav jaiswal

Cluster Analysis:

Cluster Analysis is a multivariate analysis technique that seeks to organize information about variables so that relatively homogeneous groups, or "clusters," can be formed. The clusters formed with this family of methods should be highly internally homogenous (members are similar to one another) and highly externally heterogeneous (members are not like members of other clusters.

In simple terms Cluster analysis or clustering is the assignment of a set of observations into subsets (called clusters) so that observations in the same cluster are similar in some sense.

Types of clustering:

Basically there are 2 types of clustering

1. Hierarchical Clustering
2. K-Means Clustering

Hierarchical clustering creates a hierarchy of clusters which may be represented in a tree structure called a dendrogram. Hierarchical algorithm find successive clusters using previously established clusters. They are either agglomerative or divisive. Agglomerative starts with each object as a separate cluster and then combine them into successively larger clusters. Divisive starts with the whole set and proceed to divide it into successively smaller clusters.

The main outcome of a cluster analysis is a dendrogram, which is also called a tree diagram.

Distance Measurement:

An important step in most clustering is to select a distance measure, which will determine how the similarity of two elements is calculated. This will influence the shape of the clusters, as some elements may be close to one another according to one distance and farther away according to another. The most commonly used distance function is the Euclidean distance which gives the shortest distance between two objects and is measured in a straight line.

Other commonly used methods are:

City block/Manhattan distance: It is the sum of absolute differences in values for each variable.

Chebychev distance: It is the maximum absolute difference in values for any variable.

Also the best way to measure the distance between two clusters or an object and a cluster is between groups method. This method calculates the distance by considering the distances between each pair of objects in two clusters.

How to determine the number of clusters to be formed?

The number of clusters to be formed is achieved through the cut-off point which is the point at which the next object joins the cluster at a much larger distance than the distance at which the previous object joined the cluster.

Statistics associated with cluster analysis:

Agglomeration schedule: An as gives information on the objects and cases being combined at each stage of hierarchical clustering process.

Cluster centroid: it is the mean value of the variable for all the cases or objects in a particular cluster centres. The cluster centres are the initial starting points in non hierarchical clustering.

Cluster membership: it indicates the cluster to which each object or case belongs.

Dendrogram: it is a graphical device for displaying the clustering results. Vertical line represents clusters that are joined together. The position if the line on the scale represents the distance at which the clusters are joined.

Icicle diagram: it is a graphical display of clustering results so called because it resembles the row of icicles hanging from the eaves of house. The columns correspond to the objects being clustered and the row corresponds to the no. of clusters.

Classification of clustering procedure:

Uses of Cluster Analysis in Marketing: Cluster analysis has been used in marketing for a variety of purposes.

1. Segmenting the market: for e.g. customer may be clustered on the basis of benefits got from the purchase of the product. Each cluster would consist of consumers who are relatively homogeneous in terms of benefits they seek. This approach is called benefit segmentation
2. Understanding buyer behaviour: CA can be used to identify homogeneous groups of buyers and then the buying behaviour of each group can be examined separately
3. Identifying new product opportunities: by clustering brands and products, competitive sets within the market can be determined. Brands in the same cluster compete more fiercely with each other than with brands in other clusters. A firm can examine its current offering compared to those of its competitors to identify potential new product opportunity.
4. Reducing data: it can be used as a general data reduction tool to develop clusters of data that are more manageable than individual observations.

Some Statistical software used to do cluster analysis:

1)      SPSS: In SPSS the main program for hierarchical clustering of objects or cases is hierarchical clusters. For non hierarchical the K-means cluster program can be used. This program is particularly helpful for clustering a large no. of cases.

2)      SAS:  In SAS the CLUSTER program can be used for the hierarchical clustering. Non hierarchical clustering can be accomplished using SASTCLUS. For clustering of variables the VARCLUS program is used.

3)      MINITAB: In MINITAB cluster analysis can be assessed in the multi variate > cluster observation function.

Cluster analysis is not available in Excel.

Submitted by:

Vaibhav Jaiswal

Roll No: 12109