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

Eduardo Sany Laber; Lucas Murtinho

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arXiv · 1810.00029

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

Eduardo Sany Laber·Lucas Murtinho

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Abstract

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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Eduardo Sany Laber, Lucas Murtinho. 2018-09-28. Minimization of Gini impurity via connections with the k-means problem. https://arxiv.org/abs/1810.00029

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