we propose a novel radius-margin based SVM model for joint learning of feature transformation and SVM classifier, i.e., F-SVM. Compared with the existing radius-margin based SVM methods, we derive novel lower and upper bounds for the relaxation of the radius-margin ratio. Unlike MR-SVM [@do2009feature], R-SVM$^{+}$ [@do2013convex] and RSVM$_{\mu}^{+}$ [@do2013convex] which are suggested for joint feature weighting and SVM learning, F-SVM can simultaneously learn feature transformation ${\bf L}$ and classifier $( {\bf w}, b )$. Compared with the existing metric learning for SVM methods, our F-SVM model considers both the radius and the margin information, and is convex. Then, an alternating minimization algorithm is proposed to solve our F-SVM model, which iterates by updating feature transformation and classifier alternatively. Note that kernel SVM is equivalent to perform linear SVM in the kernel PCA space. We further suggest to conduct linear FSVM in the kernel PCA space for joint learning of nonlinear transformation and classifier. The contribution of this paper is of three-fold:

-   A novel convex formulation of radius-margin based SVM model, i.e., F-SVM, is proposed. Unlike MR-SVM [@do2009feature], R-SVM$^{+}$ [@do2013convex] and RSVM$_{\mu}^{+}$ [@do2013convex], our F-SVM is capable of joint learning feature transformation and classifier, and is robust against outliers. Experimental 