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R Statistical Application Development by Example Beginner's Guide by Prabhanjan Narayanachar Tattar

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The construction of a classification tree

We first need to set up the splitting criteria for a classification tree. In the case of a regression tree, we saw the sum of squares as the splitting criteria. For identifying the split for a classification tree, we need to define certain measures known as impurity measures. The three popular measures of impurity are Bayes error, the cross-entropy function, and Gini index. Let p denote the percentage of success in a dataset of size n. The formulae of these impurity measures are given in the following table:

Measure

Formula

Bayes error

The construction of a classification tree

The cross-entropy measure

Gini index

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