Minimization of Gini impurity via connections with the k-means problem
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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.
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