Exploring Kernel Machines and Support Vector Machines: Principles, Techniques, and Future Directions

Ke-Lin Du, Bingchun Jiang (), Jiabin Lu, Jingyu Hua and M. N. S. Swamy
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Ke-Lin Du: School of Mechanical and Electrical Engineering, Guangdong University of Science and Technology, Dongguan 523668, China
Bingchun Jiang: School of Mechanical and Electrical Engineering, Guangdong University of Science and Technology, Dongguan 523668, China
Jiabin Lu: Faculty of Electromechanical Engineering, Guangdong University of Technology, Guangzhou 510006, China
Jingyu Hua: School of Information and Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, China
M. N. S. Swamy: Department of Electrical and Computer Engineering, Concordia University, Montreal, QC H3G 1M8, Canada

Mathematics, 2024, vol. 12, issue 24, 1-58

Abstract: The kernel method is a tool that converts data to a kernel space where operation can be performed. When converted to a high-dimensional feature space by using kernel functions, the data samples are more likely to be linearly separable. Traditional machine learning methods can be extended to the kernel space, such as the radial basis function (RBF) network. As a kernel-based method, support vector machine (SVM) is one of the most popular nonparametric classification methods, and is optimal in terms of computational learning theory. Based on statistical learning theory and the maximum margin principle, SVM attempts to determine an optimal hyperplane by addressing a quadratic programming (QP) problem. Using Vapnik–Chervonenkis dimension theory, SVM maximizes generalization performance by finding the widest classification margin within the feature space. In this paper, kernel machines and SVMs are systematically introduced. We first describe how to turn classical methods into kernel machines, and then give a literature review of existing kernel machines. We then introduce the SVM model, its principles, and various SVM training methods for classification, clustering, and regression. Related topics, including optimizing model architecture, are also discussed. We conclude by outlining future directions for kernel machines and SVMs. This article functions both as a state-of-the-art survey and a tutorial.

Keywords: support vector machine; kernel machine; kernel method; support vector regression; support vector clustering (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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