Clustering on imbalanced data that has high correlation
When you have high correlation problems you should go for dimensionality reduction. Multicollinear features can be "summarized" and controlled for by techniques such as PCA or Autoencoders for dimensionality reduction. I don't recomment PCA, since it can only extract factors that linearly associated with your data. In my opinion:

Autoencoders  &gt;  PCA


There are many other dimensionality reduction techniques, but these are the most common.

Once you have reduced the dimensionality of your data you can run your cluster analysis on the reduced dataset, and observe how different observations (and their categories) will be distributed with respect to each other.

Hope this helps, otherwise let me know.