my goal is to run several methods of cluster analysis with those methods following different approaches. If as you say there are clustering methods for categorical variables that depend on the type of input, number of samples, correlation, etc please let me know those methods, that is what I'm trying to ask.
Categorical variables are restrictive enough, they are defined as
A categorical variable is a category or type. For example, hair color is a categorical value or hometown is a categorical variable. Species, treatment type, and gender are all categorical variables.
A categorical variable can be expressed as a number for the purpose of statistics, but these numbers do not have the same meaning as a numerical value* . For example, if I am studying the effects of three different medications on an illness, I may name the three different medicines, medicine 1, medicine 2, and medicine 3. However, medicine three is not greater, or stronger, or faster than medicine one. These numbers are not meaningful.
Please let me know if you are aware of methods or strategies for clustering these types of variables.