Data Mining Techniques for Segmentation - Data Mining Techniques in CRM: Inside Customer Segmentation - page 73

The proportion of variance of a field that can be interpreted by another
field is represented by the square of their correlation. The eigenvalue of
each component is the sum of squared loadings (correlations) across all input
fields. Thus, each eigenvalue denotes the total variance or total information
interpreted by the respective component.
Since a single standardized field contains one unit of information, the
total information of the original fields is equal to their number. The ratio
of the eigenvalue to the total units of information (11 in our case) gives the
percentage of variance that each component represents.
By comparing the eigenvalue to the value of 1 we examine if a component
is more useful and informative than a single input.
Although the eigenvalue criterion is a good starting point for selecting the
number of fields to extract, other criteria should also be evaluated before reaching
the final decision. A list of commonly used criteria follows:
1. The eigenvalue (or latent root) criterion: This was discussed in the previous
section. Typically the eigenvalue is compared to 1 and only components with
eigenvalues higher than 1 are retained.
2. The percentage of variance criterion: According to this criterion, the
number of components to be extracted is determined by the total explained
percentage of variance. A successive number of components are extracted, until
the total explained variance reaches a desired level. The threshold value for
extraction depends on the specific situation, but, in general, a solution should
not fall below 60-65%.
3. The interpretability and business meaning of the components: The
derived factors should, above all, be directly interpretable, understandable,
and useful. Since they will be used for subsequent modeling and reporting
purposes, we should be able to recognize the information which they convey.
A component should have a clear business meaning, otherwise it is of little
value for further usage. In the next section we will present a way to interpret
components and to recognize their meaning.
4. The scree test criterion: Eigenvalues decrease in descending order along
with the order of the component extraction. According to the scree test criterion,
we should look for a large drop, followed by a ''plateau'' in the eigenvalues,
which indicates a transition from large to small values. At that point, the unique
variance (variance attributable to a single field) that a component carries starts
to dominate the common variance. This criterion is graphically illustrated by
the scree plot which displays the eigenvalues against the number of extracted
components. The scree plot for our example is presented in Figure 3.1. What