A robust version of reduced and factorial k-means is proposed that is based on the idea of trimming. Reduced and factorial k-means are data reduction techniques well suited for simultaneous dimension and sample reduction through PCA and clustering. The occurrence of data inadequacies can invalidate standard analyses. Actually, contamination in the data at hand can hide the underlying clustered structure of the data. An appealing approach to develop robust counterparts of factorial and reduced k-means is given by impartial trimming. The idea is to discard a fraction of observations that are selected as the most distant from the centroids. The finite sample behavior of the proposed methods has been investigated by some numerical studies and real data examples.

中文翻译：

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一种用于联合尺寸和样本减少的公正修整方法

提出了基于修剪思想的简化和阶乘 k 均值的稳健版本。降维和阶乘 k 均值是数据降维技术，非常适合通过 PCA 和聚类同时降维和样本降维。数据不充分的发生会使标准分析无效。实际上，手头数据中的污染可以隐藏数据的底层聚类结构。通过公正修整给出了一种有吸引力的方法来开发阶乘和减少 k 均值的稳健对应物。这个想法是丢弃一部分被选为距离质心最远的观察结果。已通过一些数值研究和实际数据示例研究了所提出方法的有限样本行为。