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December 2010 Multicategory vertex discriminant analysis for high-dimensional data
Tong Tong Wu, Kenneth Lange
Ann. Appl. Stat. 4(4): 1698-1721 (December 2010). DOI: 10.1214/10-AOAS345

Abstract

In response to the challenges of data mining, discriminant analysis continues to evolve as a vital branch of statistics. Our recently introduced method of vertex discriminant analysis (VDA) is ideally suited to handle multiple categories and an excess of predictors over training cases. The current paper explores an elaboration of VDA that conducts classification and variable selection simultaneously. Adding lasso (1-norm) and Euclidean penalties to the VDA loss function eliminates unnecessary predictors. Lasso penalties apply to each predictor coefficient separately; Euclidean penalties group the collective coefficients of a single predictor. With these penalties in place, cyclic coordinate descent accelerates estimation of all coefficients. Our tests on simulated and benchmark real data demonstrate the virtues of penalized VDA in model building and prediction in high-dimensional settings.

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Tong Tong Wu. Kenneth Lange. "Multicategory vertex discriminant analysis for high-dimensional data." Ann. Appl. Stat. 4 (4) 1698 - 1721, December 2010. https://doi.org/10.1214/10-AOAS345

Information

Published: December 2010
First available in Project Euclid: 4 January 2011

zbMATH: 1220.62086
MathSciNet: MR2829933
Digital Object Identifier: 10.1214/10-AOAS345

Keywords: Bayes’ rule , ‎classification‎ , Coordinate descent , Euclidean penalty , lasso penalty , regular simplex , Support vector machines , Variable selection

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.4 • No. 4 • December 2010
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