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Geometric representation of high dimension, low sample size data

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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

Document Type: Research Article


Affiliations: 1: Australian National University, Canberra, Australia 2: University of North Carolina, Chapel Hill, USA

Publication date: 2005-06-01

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