BibTeX
@MISC{Zhang_variableselection,
author = {Hao Helen Zhang},
title = {Variable Selection for SVM via Smoothing Spline ANOVA},
year = {}
}
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Abstract
It is well-known that the support vector machine paradigm is equivalent to solv-ing a regularization problem in a reproducing kernel Hilbert space. The squared norm penalty in the standard support vector machine controls the smoothness of the classifi-cation function. We propose, under the framework of smoothing spline ANOVA models, a new type of regularization to conduct simultaneous classification and variable selection in the SVM. The penalty functional used is the sum of functional component norms, which automatically applies soft-thresholding operations to functional components hence yields sparse solutions. We suggest an efficient algorithm to solve the proposed optimiza-tion problem by iteratively solving the quadratic programming and linear programming. Numerical studies, on both simulated data and real datasets, show that the modified support vector machine gives very competitive performances compared to other popular classification algorithms, in terms of both classification accuracy and variable selection.
Keyphrases
variable selection smoothing spline anova spline anova model soft-thresholding operation linear programming regularization problem functional component norm modified support vector machine classifi-cation function penalty functional simultaneous classification efficient algorithm support vector machine paradigm standard support vector machine real datasets squared norm penalty numerical study popular classification algorithm new type classification accuracy quadratic programming reproducing kernel hilbert space competitive performance optimiza-tion problem
