# Quadratic Surface Support Vector Machine with L1 Norm Regularization

arXiv: https://arxiv.org/abs/1908.08616 · HTML: https://mlsanity.com/paper/1908.08616/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2019.

## Built on by (most cited first, 4 of 4)

- [Sparse Universum Quadratic Surface Support Vector Machine Models for Binary Classification](https://mlsanity.com/paper/2104.01331/) (2021)
- [Kernel-Free Universum Quadratic Surface Twin Support Vector Machines for Imbalanced Data](https://mlsanity.com/paper/2412.01936/) (2024)
- [L0-Regularized Quadratic Surface Support Vector Machines](https://mlsanity.com/paper/2501.11268/) (2025)
- [A family of spectral conjugate gradient algorithms derived by least-squares approximations based on a modified quasi--Newton update with application to a revised robust binary classification model](https://mlsanity.com/paper/2609.13526/) (2026)

## Abstract (arXiv)

We propose ℓ1 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 ℓ1 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.