How to handle categorical and non-euclidean data in GMM model?

Question

What transformation measure needs to be taken for "only categorical" and "mix of numeric and categorical" and "Non-Euclidean data" for Gaussian mixture models? Does GMM only work on numerical data?

Answer 1

Gaussian Mixture Modeling obviously only works for numerical data, because the Gaussian distribution is over R.

However you can essentially do the same with other distributions such as multinomial or binomial; even mixed (at least if you assume feature independence it's trivial).