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Geometric Representation of High Dimension, Low Sample Size Data

Peter Hall, J. S. Marron and Amnon Neeman
Journal of the Royal Statistical Society. Series B (Statistical Methodology)
Vol. 67, No. 3 (2005), pp. 427-444
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/3647669
Page Count: 18
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Geometric Representation of High Dimension, Low Sample Size Data
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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.

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