Clustering in high-dimensional data: How do you compare clusters?

Question

If I perform clustering in high-dimensional data, what kind of techniques can I use to compare the resulting clusters?

e.g. if I assume that my cluster centroids are good representation of stereotypical users in some survey data, how should I compare the centroids to gain insights into how they differ qualitatively?

Edit: Of course, if I start with a concrete hypothesis regarding particular dimensions, I could simply project the centroids on these dimensions but I'm assuming I either don't have a hypothesis or I have reasons to believe that my hypothesis is incomplete.

Answer 1

I've had to do similar things and my approach (perhaps naive, certainly not sophisticated) was to just look at the means, sds, IQRs and so on of the the variables in each cluster and try to make sense of it all, usually in consultation with my "client" (sometimes an actual client, sometimes a boss).

I think cluster analysis is often like that.