Quadratic Surface Support Vector Machine with L1 Norm Regularization
This work addresses binary classification problems in supervised learning, offering an incremental improvement by combining quadratic surfaces with L1 regularization for potential sparsity benefits.
The authors tackled binary classification by proposing L1 norm regularized quadratic surface support vector machines, establishing theoretical properties like solution uniqueness and sparsity detection, and demonstrated practical efficiency with numerical experiments on synthetic and benchmark datasets.
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.