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Li, Bing; Kim, Min Kyung; Altman, Naomi

On dimension folding of matrix- or array-valued statistical objects. (English) Zbl 1183.62091

Ann. Stat. 38, No. 2, 1094-1121 (2010).
Summary: 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.
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.

Cited in 1 Review
Cited in 47 Documents

MSC:

62H12 Estimation in multivariate analysis
62G08 Nonparametric regression and quantile regression
62A09 Graphical methods in statistics
92C55 Biomedical imaging and signal processing
62H99 Multivariate analysis

Keywords:

directional regression; electroencephalography; Kronecker envelope; sliced inverse regression; sliced average variance estimate
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References:

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