Building Sparse Multiple-Kernel SVM Classifiers

The support vector machines (SVMs) have been very successful in many machine learning problems. However, they can be slow during testing because of the possibly large number of support vectors obtained. Recently, Wu et al. (2005) proposed a sparse formulation that restricts the SVM to use a small number of expansion vectors. In this paper, we further extend this idea by integrating with techniques from multiple-kernel learning (MKL). The kernel function in this sparse SVM formulation no longer needs to be fixed but can be automatically learned as a linear combination of kernels. Two formulations of such sparse multiple-kernel classifiers are proposed. The first one is based on a convex combination of the given base kernels, while the second one uses a convex combination of the so-called "equivalent" kernels. Empirically, the second formulation is particularly competitive. Experiments on a large number of toy and real-world data sets show that the resultant classifier is compact and accurate, and can also be easily trained by simply alternating linear program and standard SVM solver.