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Geometric representation of high dimension, low sample size data. (English) Zbl 1069.62097
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.

MSC:
62P10Applications of statistics to biology and medical sciences
62P99Applications of statistics
62H99Multivariate analysis