Open Access
2010 Sparse supervised dimension reduction in high dimensional classification
Junhui Wang, Lifeng Wang
Electron. J. Statist. 4: 914-931 (2010). DOI: 10.1214/10-EJS572


Supervised dimension reduction has proven effective in analyzing data with complex structure. The primary goal is to seek the reduced subspace of minimal dimension which is sufficient for summarizing the data structure of interest. This paper investigates the supervised dimension reduction in high dimensional classification context, and proposes a novel method for estimating the dimension reduction subspace while retaining the ideal classification boundary based on the original dataset. The proposed method combines the techniques of margin based classification and shrinkage estimation, and can estimate the dimension and the directions of the reduced subspace simultaneously. Both theoretical and numerical results indicate that the proposed method is highly competitive against its competitors, especially when the dimension of the covariates exceeds the sample size.


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Junhui Wang. Lifeng Wang. "Sparse supervised dimension reduction in high dimensional classification." Electron. J. Statist. 4 914 - 931, 2010.


Published: 2010
First available in Project Euclid: 15 September 2010

zbMATH: 1329.62292
MathSciNet: MR2721038
Digital Object Identifier: 10.1214/10-EJS572

Primary: 62H30

Keywords: Dimension reduction , large-p-small-n , SAVE , SIR , Support Vector Machine , tuning

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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