We introduce usage of a reduction property of penalty-based formulation of
pseudo-Boolean polynomials as a mechanism for invariant dimensionality
reduction in cluster analysis processes. In our experiments, we show that
multidimensional data, like 4-dimensional Iris Flower dataset can be reduced to
2-dimensional space while the 30-dimensional Wisconsin Diagnostic Breast Cancer
(WDBC) dataset can be reduced to 3-dimensional space, and by searching lines or
planes that lie between reduced samples we can extract clusters in a linear and
unbiased manner with competitive accuracies, reproducibility and clear
interpretation.

通过惩罚项形式的拟布尔多项式的减法性质，我们在聚类分析过程中引入了一种不变维数减少机制。在我们的实验中，我们展示了多维数据，如 4 维的鸢尾花数据集可以被减少到 2 维的空间，30 维的威斯康星州诊断性乳腺癌数据集可以被减少到 3 维的空间，并且通过搜索位于减少样本之间的线或平面，我们可以以线性、无偏的方式提取出具有竞争准确性、可重复性和清晰解释的聚类。