Novel non-Kernel quadratic surface support vector machines based on optimal margin distribution

Zhou, Jingyue; Tian, Ye; Luo, Jian; Zhai, Qianru

doi:10.1007/s00500-022-07354-8

Cited by 7 publications

(2 citation statements)

References 23 publications

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“…Furthermore, the choice of kernel parameters in kernel methods brings a computational burden. Significantly, Luo et al [31] and Zhou et al [32] have also researched the combination of kernel-free techniques with optimal margin distribution, yielding favorable performance.…”

Section: Introductionmentioning

confidence: 99%

Quadratic hyper-surface kernel-free large margin distribution machine-based regression and its least-square form

He,

Wang,

Jiang

et al. 2024

Mach. Learn.: Sci. Technol.

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ǫ-Support vector regression (ǫ-SVR) is a powerful machine learning approach that focuses on minimizing the margin, which represents the tolerance range between predicted and actual values. However, recent theoretical studies have highlighted that simply minimizing structural risk does not necessarily result in well margin distribution. Instead, it has been shown that the distribution of margins plays a more crucial role in achieving better generalization performance. Furthermore, the kernel-free technique oﬀers a signiﬁcant advantage as it eﬀectively reduces the overall running time and simpliﬁes the parameter selection process compared to the kernel trick. Based on existing kernel-free regression methods, we present two eﬃcient and robust approaches named quadratic hyper-surface kernel-free large margin distribution machine-based regression(QLDMR) and quadratic hyper-surface kernel-free least squares large margin distribution machine-based regression(QLSLDMR). The QLDMR optimizes the margin distribution by considering both ǫ-insensitive loss and quadratic loss function similar to the large-margin distribution machine-based regression (LDMR). QLSLDMR aims to reduce the cost of the computing process of QLDMR, which transforms inequality constraints into an equality constraint inspired by least squares support vector machines (LSSVR). Both models are combined the spirit of optimal margin distribution with kernel-free technique and after simpliﬁcation are convex so that they can be solved by some classical methods. Experimental results demonstrate the superiority of the optimal margin distribution combined with the kernel-free technique in robustness, generalization, and eﬃciency.

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Section: Introductionmentioning

confidence: 99%

Quadratic hyper-surface kernel-free large margin distribution machine-based regression and its least-square form

He,

Wang,

Jiang

et al. 2024

Mach. Learn.: Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…Based on the idea of quadratic kernel-free support vector machine (QSSVC) [23], Gao et al [24] proposed a kernel-free fuzzy reduced quadratic surface ν-support vector machine for Alzheimer's disease classification. Zhou et al [25] proposed a kernel-free QSSVC . For the regression problem, Ye et al [26,27] proposed two kernel-free nonlinear regression models, quadratic surface kernel-free least squares SVR (QLSSVR) and -kernel-free soft QSSVR ( -SQSSVR), respectively.…”

Section: Introductionmentioning

confidence: 99%

Kernel-Free Quadratic Surface Support Vector Regression with Non-Negative Constraints

Wang

Yang

et al. 2023

Entropy

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In this paper, a kernel-free quadratic surface support vector regression with non-negative constraints (NQSSVR) is proposed for the regression problem. The task of the NQSSVR is to find a quadratic function as a regression function. By utilizing the quadratic surface kernel-free technique, the model avoids the difficulty of choosing the kernel function and corresponding parameters, and has interpretability to a certain extent. In fact, data may have a priori information that the value of the response variable will increase as the explanatory variable grows in a non-negative interval. Moreover, in order to ensure that the regression function is monotonically increasing on the non-negative interval, the non-negative constraints with respect to the regression coefficients are introduced to construct the optimization problem of NQSSVR. And the regression function obtained by NQSSVR matches this a priori information, which has been proven in the theoretical analysis. In addition, the existence and uniqueness of the solution to the primal problem and dual problem of NQSSVR, and the relationship between them are addressed. Experimental results on two artificial datasets and seven benchmark datasets validate the feasibility and effectiveness of our approach. Finally, the effectiveness of our method is verified by real examples in air quality.

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Fuzzy large margin distribution machine for classification

Dong,

Feng,

Kurths

et al. 2023

Int. J. Mach. Learn. & Cyber.

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Novel non-Kernel quadratic surface support vector machines based on optimal margin distribution

Cited by 7 publications

References 23 publications

Quadratic hyper-surface kernel-free large margin distribution machine-based regression and its least-square form

Quadratic hyper-surface kernel-free large margin distribution machine-based regression and its least-square form

Kernel-Free Quadratic Surface Support Vector Regression with Non-Negative Constraints

Fuzzy large margin distribution machine for classification

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