I'm working on a problem where observations are being clustered within groups but I'd also like to compare the groups. However I am not sure of the best way to compare the groups.
In total I have about 1,000 groups each containing 5 clusters created using k-means. The clusters are based on anywhere from 100-10,000 data points.
For a single group, I can examine the clusters and calculate the within- and between-cluster variation, as well as the cluster means, etc.
However since I have 1,000 groups I'm trying to find different ways I can summarize these data. For example perhaps plotting the groups' mean within-cluster variation vs. mean between-cluster variation (so there is a single point per group).
Most of my ideas are simply to take the mean of something. Are there any better/other methods for summarizing group clusters?