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I was reading the limitations of decision trees. One of them was that, for classification problems, decision trees produce only orthogonal decision boundaries. Could anyone please explain what an orthogonal decision boundary is?

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  • $\begingroup$ Where did you read this? In my answer I have to make an assumption about what "orthogonal decision boundary" means, but no one can know for sure unless they see what you're reading. $\endgroup$
    – bogovicj
    Aug 13 at 12:59
  • $\begingroup$ Actually i was reading why do we need Ensemble learning and for that there were some limitations of decision tree were given and this was one of them. $\endgroup$ Aug 13 at 17:38
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Often, every node of a decision tree creates a split along one variable - the decision boundary is "axis-aligned". The figure below from this survey paper shows this pictorially. (a) is axis-aligned: the decision boundary uses variable $x_1$ only. (b) is not axis-aligned: it uses both input variables, but is linear. (c) is non-linear and not axis-aligned.

In what you read, "orthogonal decision boundary" probably means the same thing as "axis-aligned decision boundary".

axis-aligned and other decision boundaries

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