Kernel-Free Nonlinear Support Vector Machines for Multiview Binary Classification Problems

Abstract

Multiview learning (MVL) frequently uses support vector machine- (SVM-) based models, but it can be difficult to select appropriate kernel functions and corresponding parameters. Then, by introducing kernel-free tricks, two multiview classifiers are proposed, called $C$ -multiview kernel-free nonlinear support vector machine ( $C$ -MKNSVM) and its $\nu$ -version, namely, $\nu$ -MKNSVM. They try to find a quadratic hypersurface under each view to classify the sample points and employ a consistency constraint to fuse the sample points from two views. Both the primal and dual problems of $C$ -MKNSVM and $\nu$ -MKNSVM do not involve kernel functions; thus, they are allowed to be solved directly. In addition, the relationship of solutions between the primal and dual problems is discussed in each classifier. For the $C$ -version and $\nu$ -version of MKNSVM, the meanings of their parameters and the relationship between them are analyzed in detail. The experimental results of artificial and benchmark datasets show that our methods are superior to some traditional MVL classifiers like SVM-2K, PSVM-2V, and MvTSVM, especially $\nu$ -MKNSVM.