radius $R$ was adopted, where $\mathbf{\bar{x}}$ is the mean of the training samples. Although Zhu et al. [@zhu2012learning] claimed that $R=\bar{R}$, as demonstrated in [**Theorem 1**]{} of this work, $\bar{R}$ is an upper bound of $R$. The MSVM model in [@zhu2012learning] was formulated as: $$\begin{aligned}
 \label{eq:class_MSVM}
\begin{aligned}
 \min \limits_{\mathbf{w},b,\mathbf{A}} \ \ \ \ & \frac{1}{2}\left\| \mathbf{w} \right\|_{2}^{2}+C\sum\nolimits_{i}{{{\xi }_{i}}}, \\
 s.t. \ \ \ \ & {{y}_{i}}({{\mathbf{w}}^{T}}\mathbf{A}{{\mathbf{x}}_{i}}+b)\ge 1-{{\xi }_{i}}, \forall i, \\
  \ \ \ \ & {{\xi }_{i}} \ge 0, i=1,2,\cdots ,n, \\
 \ \ \ \ & {{\left\| \mathbf{A}{{\mathbf{x}}_{i}}-\mathbf{A\bar{x}} \right\|}^{2}}\le 1,\forall i.
\end{aligned}\end{aligned}$$ Note that MSVM is non-convex and solved using gradient projection.

In this paper, we propose a novel relaxed convex model of radius-margin based SVM, i.e., F-SVM, for joint learning of feature transformation and SVM classifier. Compared with the existing radius-margin based SVM methods, F-SVM has some distinguishing features. Our F-SVM model is convex, while MSVM [@zhu2012learning] is non-convex. Unlike RMM [@shivaswamy2010maximum], the transformation in F-SVM is learned to minimize the radius of the enclosing ball of all samples rather than to only shrink the sample span along the direction perpendicular to the hyperplane. Moreover, F-SVM is also different with MR-SVM [@do2009feature], R-SVM$^{+}$ [@do2013convex] and R-SVM$_{\mu}^{+}$ [@do2013convex] 