I'm doing some research into methods for discretizing a continuous variable coupled with a binary target variable to find the optimal split points to maxamise a measure of impurity (gini/entropy).
First off I'm having some trouble coming up with google-able terms. "Optimal Split" seems to relate to choosing which variable to split on in a decision tree as opposed to how to split that variable up. Is there a defined title on this problem?
I imagine to convert a continuous variable into a binary variable I could potentially try setting a split point at each distinct value in the data and take the one that returns the maximum entropy or gini.
But to extend it beyond binary splits the search space would grow to make that method pretty expensive.
Are there any popular methods for solving this?