We propose $\ell_1$ norm regularized quadratic surface support vector machine models for binary classification in supervised learning. We establish their desired theoretical properties, including the existence and uniqueness of the optimal solution, reduction to the standard SVMs over (almost) linearly separable data sets, and detection of true sparsity pattern over (almost) quadratically separable data sets if the penalty parameter of $\ell_1$ norm is large enough. We also demonstrate their promising practical efficiency by conducting various numerical experiments on both synthetic and publicly available benchmark data sets.

翻译：我们提出$\ ell_ 1$ 规范正规化的四边支持矢量机模型,用于监督学习的二进制分类。我们确定了它们理想的理论特性,包括最佳解决方案的存在和独特性,在(几乎)线性分离数据集上减少标准SVMs,在(几乎)线性分离数据集上检测真实的宽度模式,如果(几乎)四边分离数据集的罚款参数值为$ ell_ 1$ 规范足够大的话。我们还通过在合成和可公开获得的基准数据集上进行各种数字实验,展示了它们有希望的实际效率。