Gini index
Topic of Classification trees, part of Statistical learning
Gini index
| Type | Topic |
| Taught in | Classification trees |
| Part | Statistical learning |
| Questions using it | 3 |
A node impurity, I_G(m)=\sum_g\hat p_{mg}(1-\hat p_{mg})=1-\sum_g\hat p_{mg}^2: the probability that two cases drawn at random from the node fall in different classes. It is 0 for a pure node and largest when the classes are equally represented.
In Classification trees
From Classification trees
\begin{align*} I_C(m)&=-\sum_{g=1}^G \hat p_{mg}\log\hat p_{mg}, &&\text{cross-entropy},\\ I_G(m)&=\sum_{g=1}^G \hat p_{mg}(1-\hat p_{mg}) =1-\sum_{g=1}^G \hat p_{mg}^2, &&\text{Gini index},\\ I_M(m)&=1-\hat p_{mg^*}, &&\text{misclassification rate}, \end{align*}
Used in
- Taught in Classification trees
- Questions that use it (3) — Three impurities · Which split is better? · A tree by hand
- All 7 questions on Classification trees
See also
Node impurity · Building a classification tree · Choosing a split · Invariance to a change of units · Multi-way splits and missing values · Tree size and pruning · What a fitted tree can be trusted to mean · Laboratory: prune using training cross-validation