Geometric representation of high dimension, low sample size data

• 成果类型: Article
• 署名作者: Hall, P; Marron, JS; Neeman, A
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Australian National University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2005.00510.x
• 发表日期: 2005
• 页码: 427-444
• 关键词: gene-expression patterns; asymptotic-behavior; regression; parameters

摘要

High dimension, low sample size data are emerging in various areas of science. We find a common structure underlying many such data sets by using a non-standard type of asymptotics: the dimension tends to infinity while the sample size is fixed. Our analysis shows a tendency for the data to lie deterministically at the vertices of a regular simplex. Essentially all the randomness in the data appears only as a random rotation of this simplex. This geometric representation is used to obtain several new statistical insights.