# Measuring The Discriminating Power of Clustering

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.

• Welcome to DataScienceSE. I'm not very knowledgeable about this but this could be the same evaluation problem as the one in topic modeling, so hopefully looking at a few papers in this area should give you an idea how to evaluate. Also I don't fully understand your method, do you use the words in the close context of the proper noun to represent them as a distribution? Commented Mar 17, 2022 at 2:44
• Thanks for the hint, Erwan. I have extracted all proper nouns and am trying to cluster them according to THEIR proximity to each other in the text. Since the Silmarillion is more a "History" text than a story, many of the places and characters come and go. Commented Mar 17, 2022 at 11:55