I have been reading a book about Decision Trees and it caught my attention the following part:
In case of numeric attributes, decision trees can be geometrically interpreted as a collection of hyperplanes, each orthogonal to one of the axes
I tried to look for information about this in Internet, but I did not find anything. To what the author refers in this point?
Each vertex in a decision tree is associated with a question of the form "$x_i < c$?" (or "$x_i \leq c$?"), where $x_i$ is one of the input and $c$ is a constant. The decision whether to go left or right then depends on which side of the hyperplane $x_i = c$ the input is located.
The possible hyperplanes which come up this way are not arbitrary – they are orthogonal to one of the axes; the hyperplane $x_i = c$ is orthogonal to the $x_i$ axis. An example of a different hyperplane, which cannot occur, is $x_1 - x_2 = 0$.
