Abstract
Various criteria have been proposed for deciding which split is best at a given node of a binary classification tree. Consider the question: given a goodness-of-split criterion and the class populations of the instances at a node, what distribution of the instances between the two children nodes maximizes the goodness-of-split criterion? The answers reveal an interesting distinction between the gini and entropy criterion.
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References
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Breiman, L. Technical Note: Some Properties of Splitting Criteria. Machine Learning 24, 41–47 (1996). https://doi.org/10.1023/A:1018094028462
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DOI: https://doi.org/10.1023/A:1018094028462