results show that F-SVM outperforms SVM and the existing radius-margin based SVMs.

-   In F-SVM, we derive the lower and upper bounds for the radius of minimum enclosing ball (MEB) in feature space, resulting in a novel approximation of the radius. Compared with the approximations proposed in [@do2013convex], ours is much simple and can be easily adopted in developing radius-margin based SVM models.

-   An alternating minimization algorithm is developed for solving F-SVM via iterating between gradient descent and SVM learning. Therefore, the off-the-shelf SVM solvers can be employed to improve the computational efficiency. Moreover, a semi-whitened PCA method is developed for the initialization of $ {\bf M} = {\bf L}^T {\bf L} $.

The remainder of the paper is organized as follows: Section 2 reviews the related work on the radius-margin ratio based bounds and their applications. Section 3 describes the model and algorithm of the proposed F-SVM method. Section 4 extends F-SVM to the kernelized version for nonlinear classification. Section 5 provides the experimental results on the UCI machine learning datasets and the LFW dataset. Finally, we conclude the paper in Section 6.

Related work
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The radius-margin bound not only provides theoretical explanation on the generalization performance 