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We consider dimension reduction for regression or classification in which thepredictors are matrix- or array-valued. This type of predictor arises whenmeasurements are obtained for each combination of two or more underlyingvariables--for example, the voltage measured at different channels and times inelectroencephalography data. For these applications, it is desirable topreserve the array structure of the reduced predictor (e.g., time versuschannel), but this cannot be achieved within the conventional dimensionreduction formulation. In this paper, we introduce a dimension reductionmethod, to be called dimension folding, for matrix- and array-valued predictorsthat preserves the array structure. In an application of dimension folding toan electroencephalography data set, we correctly classify 97 out of 122subjects as alcoholic or nonalcoholic based on their electroencephalography ina cross-validation sample.

On dimension folding of matrix- or array-valued statistical objects