👉 Kernel-based methods, or kernel mathematics, are a class of algorithms used in machine learning and statistical analysis that operate in a high-dimensional feature space without explicitly computing the coordinates of the data in that space. Instead, they use kernel functions to compute the similarity between data points directly in the original input space, leveraging the "kernel trick" to avoid the computational burden of high-dimensional transformations. This approach allows for effective modeling of complex, non-linear relationships by mapping data into a higher-dimensional space where it becomes linearly separable or easier to model. Common kernel functions include linear, polynomial, Gaussian (RBF), and sigmoid kernels, each suited for different types of data and problems. By focusing on inner products in the feature space, kernel methods enable powerful techniques like support vector machines (SVMs), kernel principal component analysis (KPCA), and Gaussian processes, enhancing their ability to capture intricate patterns in data.
