Feature selection for support vector machines with RBF kernel

Authors:
Quanzhong Liu;Chihau Chen;Yang Zhang;Zhengguo Hu
Affiliations:
College of Mechanical and Electric Engineering, Northwest A & F University, Yangling, China 712100;Electrical & Computer Engineering, University of Massachusetts Dartmouth, Dartmouth, USA 02747-2300;College of Information Engineering, Northwest A & F University, Yangling, China 712100;College of Mechanical and Electric Engineering, Northwest A & F University, Yangling, China 712100
Venue:
Artificial Intelligence Review
Year:
2011

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Abstract

Linear kernel Support Vector Machine Recursive Feature Elimination (SVM-RFE) is known as an excellent feature selection algorithm. Nonlinear SVM is a black box classifier for which we do not know the mapping function $${\Phi}$$ explicitly. Thus, the weight vector w cannot be explicitly computed. In this paper, we proposed a feature selection algorithm utilizing Support Vector Machine with RBF kernel based on Recursive Feature Elimination(SVM-RBF-RFE), which expands nonlinear RBF kernel into its Maclaurin series, and then the weight vector w is computed from the series according to the contribution made to classification hyperplane by each feature. Using $${w_i^2}$$ as ranking criterion, SVM-RBF-RFE starts with all the features, and eliminates one feature with the least squared weight at each step until all the features are ranked. We use SVM and KNN classifiers to evaluate nested subsets of features selected by SVM-RBF-RFE. Experimental results based on 3 UCI and 3 microarray datasets show SVM-RBF-RFE generally performs better than information gain and SVM-RFE.