Cluster Exemplars 

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For any classification of cases into clusters, the cluster exemplar is that case which is in some sense most typical of the cluster.  The best way to describe the need for this is when we are profiling a cluster model; for example:

    "The cluster mean for family size was 0.75 children, as against a mean of 2.2 for the whole survey."

This interpretation of a cluster helps us quite a lot - obviously the cluster contains a fair number of families with one or no children, smaller than the whole population.  But it's difficult to build up a pen picture of the type of family which has, on average, of a child!

Cluster exemplars help us out here by selecting one typical case which is most representative of the cluster; in a sense, the modal case ..

    "The typical cluster member was [Mr and Mrs Paul Briggs] a family with one child, homeowners, income of $75,000,  ..."

We can relate much more easily to the family of Mr and Mrs Briggs than we can to a cluster mean expressed in fractions or percentages.  If needs be, we can use Mr and Mrs Briggs as a hypothetical class target, e.g. for targeted niche marketing or in customer retention management.

Sampling Frames

In another example, we might wish to design a sampling frame for national opinion polling.  The areas or constituencies under consideration are first clustered into similar types.  We can then extract the exemplars for each cluster of constituencies and sample opinions in the exemplar areas.  Furthermore, as we can measure the population sizes of each cluster, it is a simple matter to derive population estimates from the survey statistics, together with their standard errors.

ClustanGraphics offers two methods of finding cluster exemplars, according to whether we have data or proximities.  When using data, the exemplar is the case closest to the cluster mean.  We can also use k-means to cluster around exemplars, rather than to cluster means.

When using proximities, the exemplar is the case which has the highest mean similarity with all the other members of the cluster; or the lowest mean dissimilarity, if using euclidean distance.