\frac{1}{2}\left( {{\mathbf{w}}^{T}}{{\mathbf{M}}^{-1}}\mathbf{w} \right)+C\sum\limits_{i=1}^{n}{{{\xi}_{i}}}+\rho tr\left( \mathbf{M}{{\mathbf{S}}_{f}} \right), \\
 s.t.  \ \ \ \ & {{y}_{i}}({{\mathbf{w}}^{T}}{{\mathbf{f}}_{i}}+b)\ge 1-{{\xi }_{i}}, \forall i,\\
 \ \ \ \ & {{\xi }_{i}}\ge 0,i=1,2,\cdots ,n, \\
 \ \ \ \ & \mathbf{M}\succ 0.
\end{aligned}\end{aligned}$$ where ${{\mathbf{S}}_{f}}=\sum\nolimits_{i=1}^{n}{{{\mathbf{f}}_{i}}\mathbf{f}_{i}^{T}}$. [**Algorithm 1**]{} can be adopted to solve the model in Eq. (27). In our implementation, instead of using all the eigenvectors, we also consider to employ the PCA eigenvectors corresponding to first [*d*]{} largest eigenvalues, i.e., $\mathbf{W}=\left[ {{\mathbf{w}}_{1}},{{\mathbf{w}}_{2}},...,{{\mathbf{w}}_{D}} \right]$, and Section 5.2 reports the empirical result on the influence of [*d*]{} on classification accuracy.

Experiments
===========

In this section, we use both the UCI machine learning datasets and the Labeled Faces in the Wild (LFW) database to evaluate the proposed F-SVM method, and compare our F-SVM with the competing methods, including SVM and several representative radius-margin based SVM methods, i.e., RMM [@shivaswamy2010maximum], R-SVM$^{+}$ [@do2013convex] and R-SVM$_{\mu}^{+}$ [@do2013convex]. MR-SVM [@do2009feature] and MSVM [@zhu2012learning] are not considered in our experiments because their source codes are not publicly available. The 10-fold cross validation (CV) is adopted to determine the optimal values of hyper-parameters for each method. The mean classification accuracy is adopted by averaging the 100 runs of the 10-fold CV. The methods are evaluated 