@jjerphan apologies for not being more formal, but there are some other metrics that may be more applicable or accurate, compared to the ones currently in SciKit-Learn. The comment noted has some libraries that have written such metrics in Python, and also there are already existing issues that showed some metrics are academically significant.
#11369 (comment) #6654

Thank you, @BrandonKMLee, for clarifying your intends a bit.

If existing packages are interoperable with scikit-learn and contain proper implementations of those metrics, I think it is better using those.

Alternatively, integrating new metrics in scikit-learn might be of interest.

Probably, you could submit a Pull Request to scikit-learn proposing integrating one in?
Does that answer you request?

As a side note, you might want to check https://github.com/scikit-learn-contrib/metric-learn.

Thanks for the response @jjerphan but unfortunately metric-learn does not seem to match up with the idea of "Optimal Cluster Count", but otherwise it would be great if one can provide guides on what parameters are needed for methods of the cluster.

For some extra notes after reviewing https://github.com/clslabMSU/clustGUI/blob/master/internal_validation.py vs https://github.com/scikit-learn/scikit-learn/blob/main/sklearn/metrics/cluster/_unsupervised.py

• Are there any centroid methods in SciKit Learn?
• Why is the method for generating n_labels always atomized within calinski_harabasz_score and davies_bouldin_score

Also certain metrics snippets can be found here: https://github.com/intelligent-environments-lab/ProfileClustering/blob/master/Clustering%20Analysis/Clustering%20Validation%20Metrics.ipynb