Kimes Patrick K, Liu Yufeng, Neil Hayes David, Marron James Stephen
Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, North Carolina, U.S.A.
Department of Biostatistics, University of North Carolina at Chapel Hill, North Carolina, U.S.A.
Biometrics. 2017 Sep;73(3):811-821. doi: 10.1111/biom.12647. Epub 2017 Jan 18.
Cluster analysis has proved to be an invaluable tool for the exploratory and unsupervised analysis of high-dimensional datasets. Among methods for clustering, hierarchical approaches have enjoyed substantial popularity in genomics and other fields for their ability to simultaneously uncover multiple layers of clustering structure. A critical and challenging question in cluster analysis is whether the identified clusters represent important underlying structure or are artifacts of natural sampling variation. Few approaches have been proposed for addressing this problem in the context of hierarchical clustering, for which the problem is further complicated by the natural tree structure of the partition, and the multiplicity of tests required to parse the layers of nested clusters. In this article, we propose a Monte Carlo based approach for testing statistical significance in hierarchical clustering which addresses these issues. The approach is implemented as a sequential testing procedure guaranteeing control of the family-wise error rate. Theoretical justification is provided for our approach, and its power to detect true clustering structure is illustrated through several simulation studies and applications to two cancer gene expression datasets.
聚类分析已被证明是用于高维数据集探索性和无监督分析的一种非常有价值的工具。在聚类方法中，层次方法因其能够同时揭示多层聚类结构而在基因组学和其他领域广受欢迎。聚类分析中的一个关键且具有挑战性的问题是，所识别的聚类是代表重要的潜在结构，还是自然抽样变异的产物。在层次聚类的背景下，很少有方法被提出来解决这个问题，由于分区的自然树结构以及解析嵌套聚类层所需的多重检验，该问题变得更加复杂。在本文中，我们提出了一种基于蒙特卡罗的方法来检验层次聚类中的统计显著性，该方法解决了这些问题。该方法被实现为一种序贯检验程序，可保证控制家族式错误率。我们为该方法提供了理论依据，并通过几个模拟研究以及对两个癌症基因表达数据集的应用，说明了其检测真实聚类结构的能力。
