Journal
WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS
Volume 7, Issue 4, Pages 249-257Publisher
WILEY
DOI: 10.1002/wics.1354
Keywords
sliced inverse regression; sufficient dimension reduction; dimension folding; tensor data
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With the advancement of modern technology, array-valued data are often encountered in application. Such data can exhibit both high dimensionality and complex structures. Traditional methods for sufficient dimension reduction (SDR) are generally inefficient for array-valued data as they cannot adequately capture the underlying structure. In this article, we discuss recently developed higher-order approaches to SDR for regressions with matrix-or array-valued predictors, with a special focus on sliced inverse regressions. These methods can reduce an array-valued predictor's multiple dimensions simultaneously without losing much/any information for prediction and classification. We briefly discuss the implementation procedure for each method. (C) 2015 Wiley Periodicals, Inc.
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