Electronic Journal of Statistics

Sparse supervised dimension reduction in high dimensional classification

Junhui Wang and Lifeng Wang

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 4 (2010), 914-931.

Dates
First available in Project Euclid: 15 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1284557753

Digital Object Identifier
doi:10.1214/10-EJS572

Mathematical Reviews number (MathSciNet)
MR2721038

Zentralblatt MATH identifier
1329.62292

Subjects
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Keywords
Dimension reduction SAVE SIR large-p-small-n support vector machine tuning

Citation

Wang, Junhui; Wang, Lifeng. Sparse supervised dimension reduction in high dimensional classification. Electron. J. Statist. 4 (2010), 914--931. doi:10.1214/10-EJS572. https://projecteuclid.org/euclid.ejs/1284557753


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