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					                                         Cluster Analysis
It is a class of techniques that are used to classify objects or cases into relatively homogeneous
groups called as clusters. Objects in each cluster tend to be similar to each other and dissimilar to
objects in other clusters. Cluster analysis is also called classification analysis or numerical
taxonomy. Our focus will be concerned with clustering procedures that assign each object to one
and only one cluster. CA is comparable to FA in the objective of assessing the underlying
structure but CA is primarily used to group objects/cases and FA is primarily used to group
variables.

CA can be used in the following situations:
   1. Segmentation of the market (e.g. benefit segmentation of customers).
   2. Identifying new product opportunities (by clustering brands/products and finding gaps).
   3. Selecting test markets (by grouping markets/regions into homogeneous groups).

Note: CA has no statistical basis upon which to draw (and generalize) statistical inferences from
a sample to a population and is used primarily as an exploratory technique. The conclusions made
from one sample may change if a different sample is taken or if a different method/rule is used.
CA thus is characterized as a descriptive, a-theoretical and non-inferential.

Key Terms:

Hierarchical Procedures: Refers to step-wise clustering procedures involving a
combination/division of objects into clusters. The two methods are agglomerative and divisive
methods. The outcome is a solution which gives all possible clusters.
Non-Hierarchical Procedures: Refers to a procedure that produces only one solution. The input
to this method is a pre-specified expected number of clusters that is based on some
theory/rationale/experience. Unlike hierarchical clustering this method doesn’t produce results for
all possible number of clusters.
Agglomerative methods: these are hierarchical procedures that begin with each object or case in
a separate cluster. In each subsequent step the two object cluster that are most similar (based on
distance measure) are combined to build a new aggregate cluster. The process is repeated until all
objects are finally combined into a single cluster.
Divisive methods: Hierarchical clustering procedures that begin with all objects in a single
cluster which is then divided into two clusters that contains the most dissimilar objects. The
process continues until all objects become a unique cluster.
Dendrogram: Graphical representation of the results of hierarchical clustering procedures. It
shows graphically how the clusters are combined at each step of the agglomerative procedure.
Icicle Plot (Vertical Icicle Diagram): it is a graphical representation of clusters where the
hierarchical clustering process in the plot is depicted using columns as the objects to be clustered
and the rows as the number of clusters. This diagram is similar to an inverted dendrogram and
aids in determining the appropriate number of clusters.
Entropy group: Group of objects that don’t belong to any cluster. These are outliers which are
independent of any cluster.
Similarity/Distance coefficient matrix: it is a lower triangle matrix that contains pair-wise
distance between objects/cases
Practice Problem
A major Indian FMCG company wants to map the profile of its target audience in terms of
lifestyle, attitudes and perceptions. The company’s managers prepare with the help of their
research team, a set of 15 statements, which they feel measure many of the variables of interest.
The respondent had to agree or disagree (on a scale of 1 to 5 where 1 = strongly agree, 2 = agree,
3 = neither agree nor disagree, 4 = disagree, 5 = strongly disagree) with each statement. Identify
the clusters among the respondents.
     • I prefer to use email rather than write a letter
     • I feel that quality products are always priced high
     • I think twice before buying anything
     • Television is a major source of entertainment
     • A car is a necessity rather than a luxury
     • I prefer fast foods and ready to use products
     • People are more health conscious today
     • Entry of foreign companies has increased the efficiency of Indian companies
     • Women are active participants in purchase decision
     • I believe politicians can play a positive role
     • I enjoy watching movies
     • If I get a chance, I would like to settle abroad
     • I always buy branded products
     • I frequently go out on weekends
     • I prefer to pay by credit card than by cash
They took responses from 20 prospects and using these responses want to get an idea of the
clusters that may exist in their target audience.

 S.
 No.    V1   V2   V3   V4   V5    V6   V7   V8   V9    V10   V11    V12   V13    V14   V15
    1    1    2    3    2    4     1    1    3    2      1     1      1     1      2     3
    2    2    3    3    2    4     3    2    2    2      4     3      3     3      1     4
    3    4    4    3    3    3     3    3    5    2      5     4      2     3      1     3
    4    3    2    2    4    2     3    1    2    3      4     3      2     2      4     2
    5    1    2    2    3    1     2    2    5    2      3     2      1     2      3     2
    6    3    2    3    3    1     1    3    2    2      1     1      2     2      3     2
    7    4    4    3    2    4     5    1    2    5      3     5      3     2      3     4
    8    2    4    3    2    3     4    2    2    2      2     5      3     1      3     5
    9    2    4    5    2    4     3    3    2    3      2     4      1     2      3     4
   10    1    2    3    1    2     2    4    1    2      1     1      2     3      1     2
   11    3    3    2    1    2     1    3    1    1      3     4      3     1      2     1
   12    3    2    3    5    4     2    1    3    4      2     1      1     2      2     1
   13    2    2    2    1    1     3    2    3    4      2     1      3     2      3     3
   14    2    4    1    2    1     4    2    4    4      2     5      3     2      2     2
   15    4    4    1    3    5     5    1    5    4      2     5      2     2      2     5
   16    1    1    5    4    4     3    2    4    3      3     4      3     2      2     4
   17    2    3    4    4    3     3    3    3    3      2     4      4     1      1     1
   18    3    5    1    3    2     4    2    3    3      2     4      4     3      3     5
   19    1    2    2    2    3     2    1    3    2      1     3      3     1      2     3
   20    3    2    2    1    3     2    2    2    2      3     2      1     1      2     2

				
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posted:4/3/2010
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