  The Gini impurity is one of the measures used to select attribute in Decision
Trees/Random Forest construction. In this note we discuss connections between
the problem of computing the partition with minimum Weighted Gini impurity and
the $k$-means clustering problem. Based on these connections we show that the
computation of the partition with minimum Weighted Gini is a NP-Complete
problem and we also discuss how to obtain new algorithms with provable
approximation for the Gini Minimization problem.
