Geometric representation of high dimension, low sample size data |
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| Authors: | Peter Hall J S Marron Amnon Neeman |
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| Institution: | Australian National University, Canberra, Australia; University of North Carolina, Chapel Hill, USA; Australian National University, Canberra, Australia |
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| 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. |
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| Keywords: | Chemometrics Large dimensional data Medical images Microarrays Multivariate analysis Non-standard asymptotics |
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