Geometric representation of high dimension, low sample size data

Peter Hall; J. S. Marron; Amnon Neeman

doi:10.1111/j.1467-9868.2005.00510.x

Geometric representation of high dimension, low sample size data

Peter Hall, J. S. Marron^*, Amnon Neeman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

347 Citations (Scopus)

Abstract

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 ∞ 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.

Original language	English
Pages (from-to)	427-444
Number of pages	18
Journal	Journal of the Royal Statistical Society. Series B: Statistical Methodology
Volume	67
Issue number	3
DOIs	https://doi.org/10.1111/j.1467-9868.2005.00510.x
Publication status	Published - 2005

Access to Document

10.1111/j.1467-9868.2005.00510.x

Cite this

@article{db6270d35c09417da0938a653fc45827,

title = "Geometric representation of high dimension, low sample size data",

abstract = "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 ∞ 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.",

keywords = "Chemometrics, Large dimensional data, Medical images, Microarrays, Multivariate analysis, Non-standard asymptotics",

author = "Peter Hall and Marron, {J. S.} and Amnon Neeman",

year = "2005",

doi = "10.1111/j.1467-9868.2005.00510.x",

language = "English",

volume = "67",

pages = "427--444",

journal = "Journal of the Royal Statistical Society. Series B: Statistical Methodology",

issn = "1369-7412",

publisher = "Oxford University Press",

number = "3",

}

TY - JOUR

T1 - Geometric representation of high dimension, low sample size data

AU - Hall, Peter

AU - Marron, J. S.

AU - Neeman, Amnon

PY - 2005

Y1 - 2005

N2 - 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 ∞ 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.

AB - 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 ∞ 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.

KW - Chemometrics

KW - Large dimensional data

KW - Medical images

KW - Microarrays

KW - Multivariate analysis

KW - Non-standard asymptotics

UR - http://www.scopus.com/inward/record.url?scp=20744451888&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9868.2005.00510.x

DO - 10.1111/j.1467-9868.2005.00510.x

M3 - Article

SN - 1369-7412

VL - 67

SP - 427

EP - 444

JO - Journal of the Royal Statistical Society. Series B: Statistical Methodology

JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology

IS - 3

ER -

Geometric representation of high dimension, low sample size data

Abstract

Access to Document

Other files and links

Fingerprint

Cite this