and approximation of radius is generally adopted in the existing models [@shivaswamy2010maximum; @zhu2012learning]. Several approaches have been proposed from the perspective of radius-margin error [@do2009feature; @shivaswamy2010maximum; @zhu2012learning; @do2013convex], but most ones suffer from the limitations of computational burden and simplified forms of transformation. RMM [@shivaswamy2010maximum] only considers the spread of the data along the direction perpendicular to the classification hyperplane. Radius-margin based SVMs, e.g., MR-SVM [@do2009feature], R-SVM$^{+}$ [@do2013convex] and RSVM$_{\mu}^{+}$ [@do2013convex], are based on the constraint that the linear transformation matrix should be diagonal.

Another strategy for joint feature transformation and classifier learning is to incorporate metric learning with SVM, where metric learning can be adopted to learn a better linear transformation matrix [@xing2002distance; @zhu2012learning; @globerson2005metric; @schultz2004learning; @wang2013kernel; @shen2014efficient; @guillaumin2009you; @wang2014shrinkage; @tran2008human]. One simple approach to combine metric learning and SVM is to directly deploy the transformation obtained using metric learning into SVM. This approach, however, usually cannot lead to satisfactory performance improvement [@xu2012distance]. Therefore, other approaches have been proposed to integrate metric learning to SVM, e.g., support vector metric learning (SVML) [@xu2012distance] and metric learning with SVM (MSVM) [@zhu2012learning]. But SVML [@xu2012distance] was designed for RBF-SVM and ignored the radius information, while MSVM [@zhu2012learning] is non-convex.

In this paper, 