Robustness properties of k means and trimmed k means
Robustness properties of k means and trimmed k means
复制标题
DOI：
10.2307/2670010
复制
发表时间：
1999-09-01
影响因子：
3.7
通讯作者：
Gordaliza, A
中科院分区：
文献类型：
--
作者：
García-Escudero, LA;Gordaliza, A
广义k均值方法基于随机变量（或该随机变量的样本）与通过罚函数Phi测量的具有ii个点的集合之间的差异的最小化。在M估计设置（k = 1），罚函数，Φ，与无界导数，Psi，自然会导致非鲁棒广义k均值。然而，令人惊讶的是，缺乏鲁棒性也延伸到有界Psi的情况下，也就是说，广义k均值不继承的M估计，他们来自的鲁棒性。广义修剪ic均值方法试图对广义k均值方法进行鲁棒化，它是将fi均值思想与所谓的公正修剪过程相结合而产生的。本文从Hampel鲁棒性准则的角度研究了广义k均值和广义修剪k均值的性能，即研究了影响函数、故障点和定性鲁棒性，证实了修剪所提供的优越性。我们包括两个真实的数据集的研究，以明确广义修剪k均值的鲁棒性。
The generalized k means method is based on the minimization of the discrepancy between a random variable (or a sample of this random variable) and a set with ii points measured through a penalty function Phi. As in the M estimators setting (k = 1), a penalty function, Phi, with unbounded derivative, Psi, naturally leads to nonrobust generalized k means. However, surprisingly the lack of robustness extends also to the case of bounded Psi; that is, generalized k means do not inherit the robustness properties of the M estimator from which they came. Attempting to robustify the generalized k means method, the generalized trimmed ic means method arises from combining fi means idea with a so-called impartial trimming procedure. In this article study generalized k means and generalized trimmed k means performance from the viewpoint of Hampel's robustness criteria; that is, we investigate the influence function, breakdown point, and qualitative robustness, confirming the superiority provided by the trimming. We include the study of two real datasets to make clear the robustness of generalized trimmed k means.