Journal
ELECTRONIC JOURNAL OF STATISTICS
Volume 4, Issue -, Pages 914-931Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/10-EJS572
Keywords
Dimension reduction; SAVE; SIR; large-p-small-n; support vector machine; tuning
Categories
Funding
- NSF [DMS-1007634]
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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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