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

Bing Li, Min Kyung Kim, Naomi Altman

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


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 crossvalidation sample.

Original languageEnglish (US)
Pages (from-to)1094-1121
Number of pages28
JournalAnnals of Statistics
Issue number2
StatePublished - Apr 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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