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April 2010 On dimension folding of matrix- or array-valued statistical objects
Bing Li, Min Kyung Kim, Naomi Altman
Ann. Statist. 38(2): 1094-1121 (April 2010). DOI: 10.1214/09-AOS737


We consider dimension reduction for regression or classification in which the predictors are matrix- or array-valued. This type of predictor arises when measurements are obtained for each combination of two or more underlying variables—for example, the voltage measured at different channels and times in electroencephalography data. For these applications, it is desirable to preserve the array structure of the reduced predictor (e.g., time versus channel), but this cannot be achieved within the conventional dimension reduction formulation. In this paper, we introduce a dimension reduction method, to be called dimension folding, for matrix- and array-valued predictors that preserves the array structure. In an application of dimension folding to an electroencephalography data set, we correctly classify 97 out of 122 subjects as alcoholic or nonalcoholic based on their electroencephalography in a cross-validation sample.


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Bing Li. Min Kyung Kim. Naomi Altman. "On dimension folding of matrix- or array-valued statistical objects." Ann. Statist. 38 (2) 1094 - 1121, April 2010.


Published: April 2010
First available in Project Euclid: 19 February 2010

zbMATH: 1183.62091
MathSciNet: MR2604706
Digital Object Identifier: 10.1214/09-AOS737

Primary: 62-09 , 62G08 , 62H12

Keywords: directional regression , electroencephalography , Kronecker envelope , sliced average variance estimate , sliced inverse regression

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 2 • April 2010
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