  The generalization error bound of support vector machine (SVM) depends on the
ratio of radius and margin, while standard SVM only considers the maximization
of the margin but ignores the minimization of the radius. Several approaches
have been proposed to integrate radius and margin for joint learning of feature
transformation and SVM classifier. However, most of them either require the
form of the transformation matrix to be diagonal, or are non-convex and
computationally expensive. In this paper, we suggest a novel approximation for
the radius of minimum enclosing ball (MEB) in feature space, and then propose a
convex radius-margin based SVM model for joint learning of feature
transformation and SVM classifier, i.e., F-SVM. An alternating minimization
method is adopted to solve the F-SVM model, where the feature transformation is
updatedvia gradient descent and the classifier is updated by employing the
existing SVM solver. By incorporating with kernel principal component analysis,
F-SVM is further extended for joint learning of nonlinear transformation and
classifier. Experimental results on the UCI machine learning datasets and the
LFW face datasets show that F-SVM outperforms the standard SVM and the existing
radius-margin based SVMs, e.g., RMM, R-SVM+ and R-SVM+{\mu}.
