Let's assume that I want to train a random forest classifier which predicts 1 if variables a/b = constant and 0 otherwise. If I have enough data, it should be possible to build decision trees which do just that.
However, I wonder if there is a random forest variant which automatically tries to combine two variables in different ways to see if there are more optimal split points.
Surely, if there are only few variables, I could just generate such feature combinations beforehand and use a standard random forest implementation. However, with lots of features, this quickly becomes a problem. The random forest implementation, on the other hand, could just pick random features and combine them on the fly.
Is anybody aware of a random forest implementation which does just that or research papers about similar ideas?