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, 2005, vol. 67, issue 3, 427-444

Abstract: Summary. 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.

Date: 2005
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