the clustering of mixed data using python
There is not one optimal number of clusters. But dozens. Every heuristic will suggest a different "optimal" number for another poorly defined notion of what is "optimal" that likely has no relevancy for the problem that you are trying to solve in the first place.
Rather than being overly concerned with "optimality", rather explore and experiment more. Study what you are actually trying to achieve, and how to get this into mathematical form to be able to compute what is solving your problem, and what is solving someone else's...
I am trying to cluster a data set containing mixed data(nominal and ordinal) using k_prototype clustering based on Huang, Z.: Clustering large data sets with mixed numeric and categorical values.
my question is how to find the optimal number of clusters?