# Sparse Universum Quadratic Surface Support Vector Machine Models for Binary Classification

arXiv: https://arxiv.org/abs/2104.01331 · HTML: https://mlsanity.com/paper/2104.01331/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 3 Apr 2021.

## Builds on (most cited first, 10 of 10)

- [A Discrete Variational Recurrent Topic Model without the Reparametrization Trick](https://mlsanity.com/paper/2010.12055/) (2020)
- [Event Representation with Sequential, Semi-Supervised Discrete Variables](https://mlsanity.com/paper/2010.04361/) (2020)
- [Ultrasound Elasticity Imaging Using Physics-based Models And Learning-based Plug-And-Play Priors](https://mlsanity.com/paper/2103.14096/) (2021)
- [A Survey on Compressive Sensing: Classical Results and Recent Advancements](https://mlsanity.com/paper/1908.01014/) (2019)
- [Quadratic Surface Support Vector Machine with L1 Norm Regularization](https://mlsanity.com/paper/1908.08616/) (2019)
- [Least Sparsity of p-norm based Optimization Problems with p > 1](https://mlsanity.com/paper/1708.06055/) (2017)
- [A statistical framework for model-based inverse problems in ultrasound elastography](https://mlsanity.com/paper/2010.10729/) (2020)
- [Solution Uniqueness of Convex Piecewise Affine Functions Based Optimization with Applications to Constrained ℓ1 Minimization](https://mlsanity.com/paper/1711.05882/) (2017)
- [Finite Element Reconstruction Of Stiffness Images In MR Elastography Using Statistical Physical Forward Modeling And Proximal Optimization Methods](https://mlsanity.com/paper/2103.14632/) (2021)
- [Exact Support and Vector Recovery of Constrained Sparse Vectors via Constrained Matching Pursuit](https://mlsanity.com/paper/1903.07236/) (2019)

## Built on by (most cited first, 1 of 1)

- [Multi-task twin support vector machine with Universum data](https://mlsanity.com/paper/2206.10978/) (2022)

## Abstract (arXiv)

In binary classification, kernel-free linear or quadratic support vector machines are proposed to avoid dealing with difficulties such as finding appropriate kernel functions or tuning their hyper-parameters. Furthermore, Universum data points, which do not belong to any class, can be exploited to embed prior knowledge into the corresponding models so that the generalization performance is improved. In this paper, we design novel kernel-free Universum quadratic surface support vector machine models. Further, we propose the L1 norm regularized version that is beneficial for detecting potential sparsity patterns in the Hessian of the quadratic surface and reducing to the standard linear models if the data points are (almost) linearly separable. The proposed models are convex such that standard numerical solvers can be utilized for solving them. Nonetheless, we formulate a least squares version of the L1 norm regularized model and next, design an effective tailored algorithm that only requires solving one linear system. Several theoretical properties of these models are then reported/proved as well. We finally conduct numerical experiments on both artificial and public benchmark data sets to demonstrate the feasibility and effectiveness of the proposed models.