of SVM [@vapnik1998statistical], but also has been extensively adopted for improving kernel classification methods, e.g., model selection [@chapelle2002choosing; @sydorov2014deep], multiple kernel learning (MKL) [@gai2010learning; @do2009margin; @liu2013efficient; @liu2014efficient], and mapping of nominal attributes [@peng2014improved]. Denote a training set by $\mathcal{S}=\left\{ \left( {{\mathbf{x}}_{1}},{{y}_{1}} \right),...,\left( {{\mathbf{x}}_{n}},{{y}_{n}} \right) \right\}$ and a feature space by $\mathcal{H} : \Phi \left( \mathbf{x} \right)$. In [@gai2010learning; @do2009margin], the radius ${R}$ of minimum enclosing ball (MEB) in feature space is computed as: $$\begin{aligned}
 \label{eq:class_R}
\min_{ {R}, {\mathbf{x}}_{0} } {R} ^{2}, s.t. \| \Phi ({{\mathbf{x}}_{i}})-\Phi ({{\mathbf{x}}_{0}}) \|_{2}^{2} \le {{R}^{2}},i=1,2,\cdots ,n.\end{aligned}$$ Assuming that the training set is separable, given the optimal hyperplane $( {\bf w}, b )$, Vapnik [@vapnik1998statistical] suggested a radius-margin error bound which showed that the expectation of the misclassification probability depends on ${R}^{2} \| {\mathbf{w}} \|_{2}^{2}$.

The standard SVM is known as a max-margin method which only considers the margin $1/\| {\mathbf{w}} \|_{2}^{2}$ in the algorithm. When the feature space is fixed, the radius is a constant and can thus be ignored. But in many classification tasks, the model parameters [@chapelle2002choosing], combination of basis kernels [@do2009margin], feature reweighting or transformation [@weston2000feature] usually should be learned or tuned based on the training data, where integration of radius has been 