Liu, Yufeng; Hayes, David Neil; Nobel, Andrew; Marron, J. S. Statistical significance of clustering for high-dimension, low-sample size data. (English) Zbl 1205.62079 J. Am. Stat. Assoc. 103, No. 483, 1281-1293 (2008). Summary: Clustering methods provide a powerful tool for the exploratory analysis of high-dimension, low-sample size (HDLSS) data sets, such as gene expression microarray data. A fundamental statistical issue in clustering is which clusters are “really there,” as opposed to being artifacts of the natural sampling variation. We propose SigClust as a simple and natural approach to this fundamental statistical problem. In particular, we define a cluster as data coming from a single Gaussian distribution and formulate the problem of assessing statistical significance of clustering as a testing procedure. This Gaussian null assumption allows direct formulation of \(p\) values that effectively quantify the significance of a given clustering. HDLSS covariance estimation for SigClust is achieved by a combination of invariance principles, together with a factor analysis model. The properties of SigClust are studied. Simulated examples, as well as an application to a real cancer microarray data set, show that the proposed method works remarkably well for assessing significance of clustering. Some theoretical results also are obtained. Cited in 27 Documents MSC: 62H30 Classification and discrimination; cluster analysis (statistical aspects) Keywords:clustering; high-dimension; low-sample size data; \(k\)-means; microarray gene expression data; \(p\) value; statistical significance Software:pvclust; SigClust PDFBibTeX XMLCite \textit{Y. Liu} et al., J. Am. Stat. Assoc. 103, No. 483, 1281--1293 (2008; Zbl 1205.62079) Full Text: DOI