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

TL;DR

This paper introduces a novel dimension reduction technique called dimension folding that preserves the array structure of matrix- or array-valued predictors, demonstrated on EEG data for classification.

Contribution

The paper proposes a new dimension folding method specifically designed for array-valued predictors, maintaining their structure during reduction, which is not addressed by existing methods.

Findings

Achieved 97/122 accuracy in classifying alcoholics using EEG data.

Preserves array structure during dimension reduction.

Effective in real-world electroencephalography data analysis.

Abstract

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.