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.

Ensemble learning and data fusion techniques play a crucial role in modern machine learning, enhancing predictive performance, robustness, and generalization. This paper provides a comprehensive survey of ensemble methods, covering foundational techniques such as bagging, boosting, and random forests, as well as advanced topics including multiclass classification, multiview learning, multiple kernel learning, and the Dempster–Shafer theory of evidence. We present a comparative analysis of ensemble learning and deep learning, highlighting their respective strengths, limitations, and synergies. Additionally, we examine the theoretical foundations of ensemble methods, including bias–variance trade-offs, margin theory, and optimization-based frameworks, while analyzing computational trade-offs related to training complexity, inference efficiency, and storage requirements. To enhance accessibility, we provide a structured comparative summary of key ensemble techniques. Furthermore, we discuss emerging research directions, such as adaptive ensemble methods, hybrid deep learning approaches, and multimodal data fusion, as well as challenges related to interpretability, model selection, and handling noisy data in high-stakes applications. By integrating theoretical insights with practical considerations, this survey serves as a valuable resource for researchers and practitioners seeking to understand the evolving landscape of ensemble learning and its future prospects.

Machine learning has become indispensable across various domains, yet understanding its theoretical underpinnings remains challenging for many practitioners and researchers. Despite the availability of numerous resources, there is a need for a cohesive tutorial that integrates foundational principles with state-of-the-art theories. This paper addresses the fundamental concepts and theories of machine learning, with an emphasis on neural networks, serving as both a foundational exploration and a tutorial. It begins by introducing essential concepts in machine learning, including various learning and inference methods, followed by criterion functions, robust learning, discussions on learning and generalization, model selection, bias–variance trade-off, and the role of neural networks as universal approximators. Subsequently, the paper delves into computational learning theory, with probably approximately correct (PAC) learning theory forming its cornerstone. Key concepts such as the VC-dimension, Rademacher complexity, and empirical risk minimization principle are introduced as tools for establishing generalization error bounds in trained models. The fundamental theorem of learning theory establishes the relationship between PAC learnability, Vapnik–Chervonenkis (VC)-dimension, and the empirical risk minimization principle. Additionally, the paper discusses the no-free-lunch theorem, another pivotal result in computational learning theory. By laying a rigorous theoretical foundation, this paper provides a comprehensive tutorial for understanding the principles underpinning machine learning.

Magnetorheological elastomers (MREs) are widely used in vibration control due to their excellent magneto-controlled mechanical properties. In this research, polyurethane-based MRE polishing pads were prepared and used for the polishing of single-crystal SiC to investigate the magneto-controlled mechanical properties, the magneto-polishing effect, and the mechanism of action thereof. The results show that the pre-structuring process is affected by parameters such as mass fraction and particle size of magnetic particles in MREs and curing magnetic field strength, different chain strings that demonstrate different magnetorheological effects are formed. The greater the mass fraction of magnetic particles and curing magnetic field strength, the more the MREs exhibit magnetorheological effects, especially so when the magnetic particles size of 3 μ m. A series of 90 min polishing experiments on single-crystal SiC with original surface roughness ( R _a ) 80 nm were conducted using an MRE pad. The results indicate that with the increase of polishing magnetic field strengths, the shear modulus of MRE polishing pads increases, the material removal rate (MRR) of the polishing process increases and R _a decreases. As the magnetic field strength is increased from 0 mT to 335 mT, the shear modulus is increased from 1.392 MPa to 1.825 MPa (an increase of 31.1%), while MRR is increased from 706.3 nm h ⁻¹ to 835.3 nm h ⁻¹ (an increase of 18.3%), R _a is decreased from 19.92 nm to 3.62 nm (an improvement in surface quality of 81.8%). The results show that the increase of the polishing magnetic field strengths changes the material modulus of the MRE polishing pads, which cause the decreases in the compressive and shear elastic deformation of the abrasive grains on the elastic substrate. This increases the positive pressure of the abrasive grains on the SiC wafer, which enhances the material-removal ability of the SiC wafer, thereby improving the surface quality of the wafer.