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引用次数: 0
摘要
我们考虑的问题是检验通过 k-means 聚类确定的观测数据聚类之间的均值差异。在这种情况下,经典的假设检验会导致 I 类错误率上升。在最近的工作中,Gao 等人(2022 年)考虑了分层聚类背景下的相关问题。遗憾的是,他们的解决方案与分层聚类的背景高度契合,因此无法应用于 k-means 聚类。在本文中,我们提出了一个 p 值,它是 k-means 算法中所有中间聚类分配的条件。我们证明,该 p 值可以控制在有限样本中使用 k-means 聚类对一对聚类的均值差异进行检验时的选择性 I 类错误,并且可以高效计算。我们将我们的建议应用于手写数字数据和单细胞 RNA 序列数据。
We consider the problem of testing for a difference in means between clusters of observations identified via -means clustering. In this setting, classical hypothesis tests lead to an inflated Type I error rate. In recent work, Gao et al. (2022) considered a related problem in the context of hierarchical clustering. Unfortunately, their solution is highly-tailored to the context of hierarchical clustering, and thus cannot be applied in the setting of -means clustering. In this paper, we propose a p-value that conditions on all of the intermediate clustering assignments in the -means algorithm. We show that the p-value controls the selective Type I error for a test of the difference in means between a pair of clusters obtained using -means clustering in finite samples, and can be efficiently computed. We apply our proposal on hand-written digits data and on single-cell RNA-sequencing data.
期刊介绍:
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