Sparse L1-norm quadratic surface support vector machine with Universum data

Moosaei, Hossein; Mousavi, Ahmad; Hladík, Milan; Gao, Zheming

doi:10.1007/s00500-023-07860-3

Cited by 6 publications

(1 citation statement)

References 35 publications

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“…Next, Gao et al [6,7] proposed two kernel-free quartic surface support vector classification (DWPSVC) for the binary and multi-class classification problems, which further improved the classification accuracy. In addition, some kernel-free classifiers are also applied to semi-supervised learning [18,23,24,30], credit scoring [12,20], universum data [13,25], and some other extended models [11,22]. Except to the above research achievements in the classification problem, kernel-free techniques have also been applied to the regression problem.…”

Section: Introductionmentioning

confidence: 99%

Kernel-free double well potential support vector regression

Wang

Yang

2023

Preprint

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In this paper, for the regression problem, a novel kernel-free support vector regression based on the double well potential function (DWPSVR) is proposed.In fact, our model applies a type of kernel-free technique, which directly find a double well potential function to fit data, so that the regression function has geometric diversity. The principle of maximizing G-margin is used to construct our optimization problem, where G-margin is independent of the data and is an approximation of the relative geometric margin. At the same time, the ε-insensitive loss function is introduced. In addition, the primal and dual problems of our model are convex quadratic programming problems, so they can be solved directly. The existence and uniqueness of the optimal solution to both primal and dual problems and some concepts of support vectors are also addressed in theoretical analysis. The 5 artificial and 10 benchmark datasets are utilized in numerical experiments. The experimental results validate that the regression function obtained by our method has geometric diversity and the comprehensive performance of our method outperforms the linear support vector regression model and two kernel-free quadratic regression models.

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Section: Introductionmentioning

confidence: 99%

Kernel-free double well potential support vector regression

Wang

Yang

2023

Preprint

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Universum parametric $$\nu $$-support vector regression for binary classification problems with its applications

2023

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Universum data sets, a collection of data sets that do not belong to any specific class in a classification problem, give previous information about data in the mathematical problem under consideration to enhance the classifiers’ generalization performance. Recently, some researchers have integrated Universum data into the existing models to propose new models which result in improved classification performance. Inspired by these Universum models, an efficient parametric $$ \nu $$ ν -support vector regression with Universum data ($$ {\mathfrak {U}} $$ U Par-$$ \nu $$ ν -SVR) is proposed in this work. This method, which finds two non-parallel hyperplanes by solving one optimization problem and considers heteroscedastic noise, overcomes some common disadvantages of the previous methods. The $$ {\mathfrak {U}} $$ U Par-$$ \nu $$ ν -SVR includes unlabeled samples that don’t belong to any class in the training process, which results in a quadratic programming problem. Two approaches are proposed to solve this problem. The first approach derives the dual formulation using the Lagrangian function and KKT conditions. Furthermore, a least squares parametric $$ \nu $$ ν -support vector regression with Universum data (named LS-$$ {\mathfrak {U}} $$ U Par-$$ \nu $$ ν -SVR) is suggested to further increase the generalization performance. The LS-$$ {\mathfrak {U}} $$ U Par-$$ \nu $$ ν -SVR solves a single system of linear equations, instead of addressing a quadratic programming problem in the dual formulation. Numerical experiments on artificial, UCI, credit card, NDC, and handwritten digit recognition data sets show that the suggested Universum model and its solving methodologies improve prediction accuracy.

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Kernel-free Reduced Quadratic Surface Support Vector Machine with 0-1 Loss Function and L$$_p$$-norm Regularization

Wu,

Yang

2024

Ann. Data. Sci.

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Sparse L1-norm quadratic surface support vector machine with Universum data

Cited by 6 publications

References 35 publications

Kernel-free double well potential support vector regression

Kernel-free double well potential support vector regression

Universum parametric $$\nu $$-support vector regression for binary classification problems with its applications

Kernel-free Reduced Quadratic Surface Support Vector Machine with 0-1 Loss Function and L$$_p$$-norm Regularization

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