Data Mining Techniques for Segmentation - Data Mining Techniques in CRM: Inside Customer Segmentation - page 72

Table 3.4 The variance explained.

Total variance explained

Components Eigenvalue % of variance Cumulative %

1 2.84 25.84 25.84

2 1.96 17.78 43.62

3 1.76 16.01 59.63

4 1.56 14.21 73.84

5 1.25 11.33 85.16

6 0.49 4.45 89.62

7 0.38 3.41 93.03

8 0.34 3.06 96.09

9 0.26 2.38 98.47

10 0.16 1.44 99.92

11 0.01 0.08 100.00

Eigenvalues can also be expressed in terms of a percentage of the total variance
of the original fields. The second column of the table denotes the proportion of
the variance attributable to each component, and the next column denotes the
proportion of the variance jointly explained by all components up to that point.
The percentage of the initial variance attributable to the five extracted components
is about 85%. This figure is not bad at all, if you consider that by keeping only 5 of
the 11 original fields we lose just a small part of their initial information.

Technical Tips on the Eigenvalue Criterion

Variance is a measure of the variability of a field. It summarizes the dispersion
of the field values around the mean. It is calculated by summing the squared
deviations from the mean (and dividing them by the total number of records
minus 1). Standard deviation is another measure of variability and is the
square root of the variance. A standardized field with the z -score method is
created with the following formula:

( Record value − mean value of field ) / standard deviation of the field .

The variance can be considered as a measure of a field's information. A
standardized field has a standard deviation and a variance value of 1, hence
it carries one unit of information.
As mentioned above, each component is related to the original fields and
these relationships are represented by the loadings in the component matrix.