Geometric representation of high dimension, low sample size data

被引：296

作者：

Hall, P

Marron, JS ^{[1
]}

Neeman, A

机构：

[1] Univ N Carolina, Dept Stat, Chapel Hill, NC 27599 USA

[2] Australian Natl Univ, Canberra, ACT, Australia

来源：

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY | 2005年 / 67卷

关键词：

chemometrics; large dimensional data; medical images; microarrays; multivariate analysis; non-standard asymptotics;

D O I：

10.1111/j.1467-9868.2005.00510.x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：427 / 444

页数：18

共 50 条

[31] Intrinsic Dimensionality Estimation of High-Dimension, Low Sample Size Data with D-Asymptotics
Yata, Kazuyoshi
Aoshima, Makoto
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2010, 39 (8-9) : 1511 - 1521
[32] A variable selection method considering cluster loading for labeled high dimension low sample size data
Chen, Jiaxin
Sato-Ilic, Mika
[J]. KNOWLEDGE-BASED AND INTELLIGENT INFORMATION & ENGINEERING SYSTEMS 19TH ANNUAL CONFERENCE, KES-2015, 2015, 60 : 850 - 859
[33] On asymptotic normality of cross data matrix-based PCA in high dimension low sample size
Wang, Shao-Hsuan
Huang, Su-Yun
Chen, Ting-Li
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2020, 175
[34] Consistency of sparse PCA in High Dimension, Low Sample Size contexts
Shen, Dan
Shen, Haipeng
Marron, J. S.
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2013, 115 : 317 - 333
[35] Boundary behavior in High Dimension, Low Sample Size asymptotics of PCA
Jung, Sungkyu
Sen, Arusharka
Marron, J. S.
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2012, 109 : 190 - 203
[36] ON SIMULTANEOUS CALIBRATION OF TWO-SAMPLE t-TESTS FOR HIGH-DIMENSION LOW-SAMPLE-SIZE DATA
Zhang, Chunming
Jia, Shengji
Wu, Yongfeng
[J]. STATISTICA SINICA, 2021, 31 (03) : 1189 - 1214
[37] Tree enhanced deep adaptive network for cancer prediction with high dimension low sample size microarray data
Wu, Yao
Zhu, Donghua
Wang, Xuefeng
[J]. APPLIED SOFT COMPUTING, 2023, 136
[38] Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting
Christoph, Gerd
Ulyanov, Vladimir V.
[J]. MATHEMATICS, 2020, 8 (07)
[39] Data maximum dispersion classifier in projection space for high-dimension low-sample-size problems
Shen, Liran
Yin, Qingbo
[J]. KNOWLEDGE-BASED SYSTEMS, 2020, 193
[40] Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix
Yata, Kazuyoshi
Aoshima, Makoto
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2010, 101 (09) : 2060 - 2077

← 1 2 3 4 5 →