2010/02/19 by Bing Li, Min Kyung Kim, Naomi Altman · 2 citations
Computer Science · Engineering · Mathematics · #Face and Expression Recognition #Neural Networks and Applications #graph theory and CDMA systems #math.ST #msc:62-09 #msc:62G08 #msc:62H12 #stat.TH
paper · pdf · doi:10.1214/09-aos737
published as Annals of Statistics 2010, Vol. 38, No. 2, 1094-1121 · Published in at http://dx.doi.org/10.1214/09-AOS737 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2010/02/19 · arxiv created 2010/02/25 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.