In this paper, a new approach in classification models, called Polarized Classification Tree model, is introduced. From a methodological perspective, a new index of polarization to measure the goodness of splits in the growth of a classification tree is proposed. The new introduced measure tackles weaknesses of the classical ones used in classification trees (Gini and Information Gain), because it does not only measure the impurity but it also reflects the distribution of each covariate in the node, i.e., employing more discriminating covariates to split the data at each node. From a computational prospective, a new algorithm is proposed and implemented employing the new proposed measure in the growth of a tree. In order to show how our proposal works, a simulation exercise has been carried out. The results obtained in the simulation framework suggest that our proposal significantly outperforms impurity measures commonly adopted in classification tree modeling. Moreover, the empirical evidence on real data shows that Polarized Classification Tree models are competitive and sometimes better with respect to classical classification tree models.

本文介绍了一种新的分类模型方法，称为极化分类树模型。从方法学的角度出发，提出了一种新的极化指数来衡量分类树生长中分裂的良好程度。新引入的度量解决了分类树中使用的经典度量（Gini和Information Gain）的弱点，因为它不仅可以度量杂质，还可以反映节点中每个协变量的分布，即，采用更具区分性的协变量进行拆分每个节点上的数据。从计算的角度出发，提出并实施了一种新算法，该新算法在树木生长中采用了新提出的措施。为了显示我们的建议如何工作，已经进行了模拟练习。在模拟框架中获得的结果表明，我们的建议明显优于分类树建模中通常采用的杂质度量。此外，实际数据的经验证据表明，极化分类树模型相对于经典分类树模型具有竞争力，有时甚至更好。