Multicategory vertex discriminant analysis for high-dimensional data

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 (${\ell }_1$-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.

Published in at http://dx.doi.org/10.1214/10-AOAS345 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (7)

• Pathwise coordinate optimization
• Coordinate descent algorithms for lasso penalized regression
• Structured variable selection and estimation
• New multicategory boosting algorithms based on multicategory Fisher-consistent losses
• Variable selection for the multicategory SVM via adaptive sup-norm regularization
• Multicategory vertex discriminant analysis for high-dimensional data
• Structured variable selection in support vector machines

Cited by in corpus (1)

• Multicategory vertex discriminant analysis for high-dimensional data