8.11 Classification trees

• Very similar to a regression tree except it predicts a qualitative (vs quantitative) response

• We predict that each observation belongs to the most commonly occurring class of training observations in the region to which it belongs

• In the classification setting, RSS cannot be used as a criterion for making the binary splits

• A natural alternative to RSS is the classification error rate, i.e., the fraction of the training observations in that region that do not belong to the most common class:

$$E = 1 - \max_k(\hat{p}_{mk})$$

where $\hat{p}_{mk}$ is the proportion of training observations in the $m$th region that are from the $k$th class

• However, this error rate is unsuited for tree-based classification because $E$ does not change much as the tree grows (lacks sensitivity)