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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?

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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 $x_1 - x_2 = 0$.

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  • $\begingroup$ thanks @Yuval Filmus, could you be so kind to recommend me some bibliography about that in a comment? Thanks $\endgroup$ – Layla Nov 2 '18 at 16:53
  • $\begingroup$ I can't think of anything in particular, unfortunately. $\endgroup$ – Yuval Filmus Nov 2 '18 at 16:55

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