# Difference between Random Forest and Random Subspaces/Patches

When fitting a Random Forest model, a subset of the features is randomly considered at the splitting of each node. E.g., if $$p$$ is the number of features, then at each node in each tree, $$\sqrt{p}$$ features are considered for splitting after being randomly drawn (with replacement?) from the feature space.

Now, with a random patches algorithm, instead of this, a subset of the features is drawn randomly from the original $$p$$ features (say $$m < p$$), and a tree is grown on this subset. In this implementation, because we are taking a subset before growing a tree, the remaining $$p - m$$ features are not considered at all when splitting at a node.

However, should the trees in a random patches method randomly draw again from the $$m$$ features at each node? Or is some other splitting procedure done, that is different from that of a random forest? Can trees be grown without any randomization?

• As far as I can tell the only difference between the two is that Random Patches is obtained by drawing random subsets of both instances and features, as opposed to Random Forests which only draws random features (by default, unless otherwise specified through argument sampsize). – user2974951 Sep 25 '18 at 6:36