I am working on a text classification problem using Random Forest as classifiers, and a bag-of-words approach. I am using the basic implementation of Random Forests (the one present in scikit), that creates a binary condition on a single variable at each split. Given this, is there a difference between using simple tf (term frequency) features. where each word has an associated weight that represents the number of occurrences in the document, or tf-idf (term frequency * inverse document frequency), where the term frequency is also multiplied by a value that represents the ratio between the total number of documents and the number of documents containing the word)?
In my opinion, there should not be any difference between these two approaches, because the only difference is a scaling factor on each feature, but since the split is done at the level of single features this should not make a difference.
Am I right in my reasoning?