Say I am discretizing continuous data based on percentiles. (I realize this is generally frowned upon, but I am doing this for the sake of experiment) I am trying different percentiles, eg breaking the data into 10 categories, or 50 or 100. We will refer the amount of percentiles chosen as P.
Is there any difference in how the learning algorithm will function if I have one feature with P possible values, or if I have P feature, each of which is binary. I feel I am more drawn to the option that would give less dimensions (due to the fact that trying to visualize what 100 dimensions might look like may void my brain's warranty), but would like to know if there is any benefit to the higher dimension approach. Or is it very case specific?
(I am looking at logistic regression and SVM)