I've been trying to wrap my head around the use of eigenvalues in cluster analysis. What does it tell me about my clustering behavior? In a typical hierarchical cluster output from using SAS, the first table given lists all of the eigenvalues.
From what I understand, eigenvalues are derived from covariance between the variables. What I fail to understand is how this would assist me in understanding the underlying clustering behavior.
Anyone know a simple answer of why the eigenvalues are important to know for cluster analysis?
Here's the output:

 A: I teach cluster analysis and it baffles me as well.  If you give PROC CLUSTER a distance matrix it does not produce this.  It is not needed and I usually therefore add the "noeigen" option otherwise, so that it is omitted.   The only reason I can think for including it is to help you understand something of the structure of the data you are giving it and how correlated the variables are. i.e. to give you a sneak look at principal components.  It does not help you pick the number of clusters. 
Before clustering you should consider if the data needs preparing in any way.  For example, outliers or highly skewed data can lead to one or two clusters with most of the observations and some other clusters with just one or two observations.  So taking a transformation of the data or removing outliers can help.   It is nearly always worth standardising the data otherwise the variables which are large values and with the most variability will dominate the clusters.
If there is a mix of variables some of which are unique and some of which are correlated with each other (e.g. age and years of employment) one way of pre-processing this is to carry out principal components. Otherwise it is as if you were using some facets of the data more than once (age approx equal year of employment +17; so having both of the these in means age is added twice).  If you use principal components first, then cluster on the first so many components this issue is avoided. That is the only reason why I can think of that SAS includes it here. So by looking at this first you can decide if you should have done this.
SAS does calculate something called the cubic clustering criteria (CCC) see this:
http://support.sas.com/documentation/onlinedoc/v82/techreport_a108.pdf
and buried in the middle of this is something about applying PCA to construct this statistic. It relates to constructing "hyper-cubes" and PCA can make this work faster.  It is mentioned in their documentation as well with reference to the CCC.   However I have yet to find any references to this criteria outside of SAS.
Personally, regarding the eigen analysis,  I leave it out.  If you do want to do PCA first then do it properly and use PRIC PRINCOMP first!  Otherwise just add the noeigen option.  That is what I get my students to do.
A: 1 shows that that factor is not dependent on other while, 0 eigen value shows it depends or has collinearlity with others.
Convert cumulative to percentage in the end its alwaz 100%
this table is used while choosing number of factor in factor analysis
Here we have a trade off b/w low eigen and high cumulative(that shows the variance amongst these factor)
we want to cover high variance and have clusters of factors that are separeted hence eigen value 1.
If you get 2 or 3 or 6 its the vector length of it :-P
