Gini Index

Measures statistical dispersion.

0 → perfect equality, all values same class 1 → maximum ineuqality

Based on Lorenz Curve.

Gini⁡(D)=1−∑j=1npj2\operatorname{Gini}(D)=1-\sum_{j=1}^{n} p_{j}^{2} ΔGini⁡A(D)=Gini⁡(D)−Gini⁡A(D)\Delta \operatorname{Gini}_{A}(D)=\operatorname{Gini}(D)-\operatorname{Gini}_{A}(D)

Attribute with minimum Ginig Index is used.

Example

Bildschirmfoto 2022-06-20 um 18.22.24.png

Disadvantages

  • Biased to multi-valued attributes
  • Has difficulties when number of classes is large
  • Tends to favor equal-sized partitions and purity in both of them