Gini Index

When building classifier decision trees, the Gini index is a metric used to determine the best way to split data at a given node. It is given by:

$$G=\sum _{k=1}^K{\hat{p}}_{mk}(1-{\hat{p}}_{mk})$$

where ${\hat{p}}_{mk}$ is the probability of observations in the $m$th region that are class $K$.

The Gini index will be small if all ${\hat{p}}_{mk}$ are close to 1 or 0. The Gini index is also sometimes referred to as a measure of node purity, since a small value indicates that the node mostly contains observations from a single class.