Quadratic surface support vector machine with L1 norm regularization

<p style='text-indent:20px;'>We propose <inline-formula><tex-math id="M1">\begin{document}$ \ell_1 $\end{document}</tex-math></inline-formula> norm regularized quadratic surface support vector machine models for binary classification in supervised learning. We establish some desired theoretical properties, including the existence and uniqueness of optimal solution, reduction to standard SVMs over (almost) linearly separable data sets, detection true sparsity pattern quadratically sets if penalty parameter on id="M2">\begin{document}$ is large enough. also demonstrate their promising practical efficiency by conducting various numerical experiments both synthetic publicly available benchmark sets.</p>