I am measuring the "proximity" of certain words (proper nouns) within a certain text (Silmarillion) by determining the occurrences of these words within the text and, via binning, creating a discrete distribution of them.
I then compare these distributions (% of occurrences per bin) with the Hellinger distance, and I run Mathematica's "FindClusters" function on the resulting distance matrix. The output shows me how the words are clustered within the text. I leave it to Mathematica to determine the number of clusters. So far, so good.
Clearly, my chosen bin width impacts the distributions which I attempt to cluster, so I was wondering if there is any measure for the discriminating power of a clustering; the maximum information content between "all elements in one cluster" and "each element is its own cluster."
I would then run a loop with increasing bin width to find the clustering telling me "the most" about the structure of the text.
A link to a source would actually suffice - I wasn't able to find anything, probably because I am not sure of the appropriate search terms.