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Fast Nonparallel Support Vector Machine with the Margin Hyper-planes and Its Iterative Solver
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DOI：10.23919/cje.2025.00.007.png)
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Abstract
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Nonparallel support vector machine (NPSVM) combines the advantages of support vector machine (SVM) and twin SVM, excelling in small-scale data classification. However, its inability to leverage the structural distribution of samples limits its generalization capability. NPSVM requires solving a pair of quadratic programming problems with inequality constraints, thereby reducing learning efficiency. To handle these draw-backs, we propose a fast NPSVM model with the margin hyper-planes (MH-fNPSVM), which introduces several key innovations. Firstly, by replacing inequality constraints with equality constraints, MH-fNPSVM transforms the optimization problem into solving a pair of linear equations, significantly improving computational efficiency. Secondly, MH-fNPSVM also incorporates margin distribution by optimizing the first and second-order statistics of the training samples, improving the generalization performance. Furthermore, MH-fNPSVM transforms the slack variables from 1-norm to 2-norm by employing a quadratic loss function, which overcomes the non-smoothness of the original loss function in NPSVM and enables the model to effectively fit the trends in data distribution, enhancing the robustness and generalization ability. Lastly, an iterative conjugate gradient method is designed for MH-fNPSVM to avoid kernel matrix inversion, thereby ensuring both accuracy and scalability. The model was validated on different datasets and demonstrated excellent performance in generalization and runtime compared to the baseline model.
Keywords:
Sonar
Aerospace and electronic systems
Electronic mail
Layered division multiplexing
Radio access networks
Regional area networks
Protocols
Radio frequency
HTTP
Communication systems
Nonparallel support vector machine
Structural distribution
Equality constraints
Steel surface defect classification
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