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In Decision Tree or Random Forest, each tree has a collection of decision nodes (in which each node has a threshold value) and a class labels (or regression values).

I know that threshold values are used for comparison with a corresponding feature value. As far as I know, the comparison is performed either "<", ">" or "==" predicate. Anything else for the functions taking threshold value and a feature value as inputs??

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For a binary split, there are only three possible operations (or arguably only two if you consider one-hot encoding). Any other kind of split would simply not be binary. Almost every tree-based model is restricted to binary splits, due to the combinatorial explosion when considering ternary or even more complex splits.

Of course you could write your own algorithm that uses recursive non-binary splits. Beware though that you'll be facing the same difficulty that has led the vast majority of algorithms to be limited to strictly binary splits.

Have a look at this related question.

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