Cancer Related Gene Identification via p-norm Support Vector Machine∗

This paper focuses on the feature selection in classification via a new version of support vector machine (SVM) named p-norm support vector machine (0 < p < 1). Different from the 2-norm in the standard linear SVM, the p-norm of the normal vector of the decision plane is used which leads to more sparse solution. By using the successive linear algorithm, we can get an approximate local optimal solution to our p-norm SVM. In addition, the lower bounds for the absolute value of nonzero components in every local optimal solution is established, which provides theoretical direction for the elimination of zero components in any numerical solution. The numerical experiments show that the p-norm SVM is effective in selecting relevant features, compared with the popular 1-norm SVM, 0-norm SVM and support vector machine-recursive feature elimination based (SVM-RFE).