\ \ & {\frac{1}{2}}\sum\nolimits_{k}\frac{w_{k}^{2}}{{\mu}_{k}}+{\frac{C}{\sum\nolimits_{k}{{{\mu }_{k}}R_{k}^{2}}}}\sum\nolimits_{i}{{{\xi }_{i}}}, \\
 s.t. \ \ \ \ & {{y}_{i}}({{{\mathbf{w}}^{T}}{{\mathbf{x}}_{i}}}+b)\ge 1-{{\xi }_{i}}, \forall i, \\
 \ \ \ \ & {{\xi }_{i}} \ge 0, i=1,2,\cdots ,n,\\
 \ \ \ \ & \sum\nolimits_{k}{{{\mu }_{k}}}=1,{{\mu }_{k}}\ge 0,\forall k.
\end{aligned}\end{aligned}$$ Denote ${{R}_{O}}$ by the half value of the maximum pairwise distances. Do et al. in [@do2013convex] introduced a tighter bound of the radius ${{R}_{O}}\le {{R}_{\mathbf{\mu }}}\le \frac{1+{\sqrt{3}}}{2}{{R}_{O}}$ and proposed another convex model R-SVM$_{\mu}^{+}$: $$\begin{aligned}
 \label{eq:class_R-SVM-mu+}
\begin{aligned}
 \min \limits_{ {\bf w},{b},{\mathbf \xi},{\mathbf \mu},{r}} \ \ \ \ & {\frac{1}{2}}\sum\nolimits_{k}\frac{w_{k}^{2}}{{\mu}_{k}}+{\lambda}{r}+ C\sum\nolimits_{i}{{{\xi }_{i}}}, \\
 s.t. \ \ \ \ & {{y}_{i}}({{\mathbf{w}}^{T}}{{\mathbf{x}}_{i}}+b)\ge 1-{{\xi }_{i}}, \forall i, \\
  \ \ \ \ & {{\xi }_{i}} \ge 0, i=1,2,\cdots ,n, \\
 \ \ \ \ & \sum\nolimits_{k}{{{\mu }_{k}}}=1,{{\mu }_{k}}\ge 0,\forall k, \\
 \ \ \ \ & \frac{1}{2}{{\left\| {{D}_{\sqrt{\mathbf{\mu }}}}{{\mathbf{x}}_{i}}-{{D}_{\sqrt{\mathbf{\mu }}}}{{\mathbf{x}}_{j}} \right\|}^{2}}\le r,\forall i,j.
\end{aligned}\end{aligned}$$ Furthermore, R-SVM$^{+}$ was developed in [@do2013convex] by controlling both the radius and margin with ${\bf w}$.

Rather than feature reweighting and selection, Zhu et al. [@zhu2012learning] proposed a metric learning with SVM (MSVM) method for joint learning of the linear transformation and SVM classifier. In [@zhu2012learning], given the transformation matrix ${\mathbf A}$, an alternative $\bar{R}={{\max }_{i}}\left\| \mathbf{A}{{\mathbf{x}}_{i}}-\mathbf{A\bar{x}} \right\|_{2}^{2}$ of the 