Brian S. Everitt A Handbook of Statistical Analyses using SPSS

The procedure continues until all individuals in a cluster are
closer to their own cluster mean vector than to that of any
other cluster.
Essentially the technique seeks to minimize the variability
within clusters and maximize variability between clusters.
Finding the optimal number of groups will also be an issue
with this type of clustering. In practice, a k-means solution is
usually found for a range of values of k, and then one of the
largely ad hoc techniques described in Everitt et al. (2001) for
indicating the correct number of groups applied.
Different methods of cluster analysis applied to the same set
of data often result in different solutions. Many methods are
really only suitable when the clusters are approximately spherical
in shape, details are given in Everitt et al. (2001).
Box 12.2 Fisher’s Linear Discriminant Function
A further aspect of the classification of multivariate data concerns
the derivation of rules and procedures for allocating
individuals/objects to one of a set of a priori defined groups
in some optimal fashion on the basis of a set of q measurements,
x 1, x 2, …, x q, taken on each individual or object.
This is the province of assignment or discrimination techniques.
The sample of observations for which the groups are known
is often called the training set.
Here we shall concentrate on the two group situation and on
the most commonly used assignment procedure, namely,
Fisher’s linear discriminant function (Fisher, 1936).
Fisher’s suggestion was to seek a linear transformation of the
variables
z a x a x a x
such that the separation between the group means on the
transformed scale, – z 1 and – z 2, would be maximized relative to
the within group variation on the z-scale.
© 2004 by Chapman & Hall/CRC Press LLC
1 1 2 2 L
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