how to calculate number of optimal clusters from a known clusters,

Question

if i want ti study a population that is clustered into 36 cluster, and want to know to optimal number of clusters that will represent the population

Answer 1

It depends on the assumptions that you have about the data and their structure...

If you have an alternative model, you could compare the models (e.g. likelihood ratio if they are nested.)

Or try a bootstrapping approach and see if/ which clusters can be replicated (cross-validation...)

You can compare models for metrics like BIC or AIC.

Also heuristics such as the elbow method could be applied (plot the explained variation as a function of number of clusters).

From a theoretical perspective, you could deduce and argue which cluster might be meaningful.