The class asked for more detail on using AIC to evaluate clustering solutions.  Here are a couple of references that we'll cover regarding AIC. 

Here are lecture notes from a class at Univ of Iowa.  We'll follow this derivation. 

ms_lec_2_ho.pdf

Here's a short paper that describes a correction to AIC when the data set is small.

aic_reg.pdf

This paper is as close as I could get to Akaike's original paper describing the technique.

10.1.1.55.7181.pdf

Here's a relatively recent survey-ish sort of paper with good references for those who need more.  This paper also has comparison with BIC (Bayesian Information Criterion)

Burnham_and_Anderson_2004_Multimodel_Inference.pdf

This paper does a comparison of AIC with BIC in the context of mixed model regression. 

BestRegression.doc