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

382 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

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10.1111/j.1467-9868.2005.00510.x

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KW - Chemometrics

KW - Large dimensional data

KW - Medical images

KW - Microarrays

KW - Multivariate analysis

KW - Non-standard asymptotics

UR - https://www.scopus.com/pages/publications/20744451888

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

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Geometric representation of high dimension, low sample size data

Abstract

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