Quadratic Surface Support Vector Machine with L1 Norm Regularization

TL;DR

This paper introduces an $ ext{L}_1$ norm regularized quadratic surface SVM model that enhances binary classification by promoting sparsity and ensuring theoretical robustness, with promising experimental results.

Contribution

It presents a novel $ ext{L}_1$ regularized quadratic surface SVM model with proven theoretical properties and demonstrated practical efficiency.

Findings

Existence and uniqueness of the optimal solution.

Reduction to standard SVMs on linearly separable data.

Effective detection of true sparsity patterns.

Abstract

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.