How to evaluate clustering success in a completely unsupervised system? The algorithm in question is Kohonen's SOM. But the question could also apply to PCA and some others.

When the umatrix (or the codebook?) is examined, is there a way to tell how successful clustering was?

And would it be a good idea to apply GA's to optimize size, lattice structure, learning rate, and the learning degradation functions as well as the epoch count for clustering, or is there a danger of overfitting in this instance?

Assume that the SOM data is coming from a demonstrably weak PRNG and that the very first attempt shows a distinct structure. Is there some statistical property or algorithm that can evaluate the presence and degree of structure to be used for a GA fitness function?
First, PCA is not a clustering method. It is a dimensionality reduction scheme.  You can assess the performance of PCA through analysis of the percent of variance in the dataset that is retained as you decrease the number of dimensions.  Retaining 99%,95%, or 90% is usually ideal, depending on your problem. 

With regards to clustering, you probably want to start with the Silhouette Coefficient.  This combines assessments of both the cohesion (how tight a cluster is) and separation (how well separated each cluster is from other clusters).


Calculate a = average distance of i to the points in its cluster
Calculate b = min (average distance of i to points in another cluster) 
The silhouette coefficient for a point is then given by:
s =1 – a/b, if a &lt; b


It is typically between 0 and 1 with larger numbers being "better".  You can average the coefficients over a cluster or the entire region to get an assessment of the cluster or the entire clustering procedure for your data.

More generally, try googling "assessing clustering" or "cluster validity" to read about all of the other ways that you can score your clustering algorithm.  Here is a very complete treatment of the topic.

Hope this helps!