Gini coefficient vs Gini impurity - decision trees The problem refers to decision trees building. According to Wikipedia 'Gini coefficient' should not be confused with 'Gini impurity'. However both measures can be used when building a decision tree - these can support our choices when splitting the set of items.

1) 'Gini impurity' - it is a standard decision-tree splitting metric (see in the link above);

2) 'Gini coefficient' - each splitting can be assessed based on the AUC criterion. For each splitting scenario we can build a ROC curve and compute AUC metric. According to Wikipedia AUC=(GiniCoeff+1)/2;

Question is: are both these measures equivalent? On the one hand, I am informed that Gini coefficient should not be confused with Gini impurity. On the other hand, both these measures can be used in doing the same thing - assessing the quality of a decision tree split.
No, despite their names they are not equivalent or even that similar. 


Gini impurity is a measure of misclassification, which applies in a multiclass classifier context. 
Gini coefficient applies to binary classification and requires a classifier that can in some way rank examples according to the likelihood of being in a positive class. 


Both could be applied in some cases, but they are different measures for different things. Impurity is what is commonly used in decision trees.