👉 The kernel method in mathematics, particularly in the context of machine learning and statistics, is a powerful tool that extends linear methods to nonlinear spaces by implicitly mapping data into a higher-dimensional feature space using a kernel function. This transformation allows for the computation of inner products between data points in this higher-dimensional space without explicitly performing the transformation, which can be computationally infeasible. The kernel function, often denoted as K(x, y), measures the similarity or distance between two data points x and y in this mapped space. Common examples include the linear kernel (which corresponds to the dot product), polynomial kernels, and radial basis function (RBF) kernels. By leveraging this implicit mapping, kernel methods can effectively capture complex patterns and nonlinear relationships in data, making them highly versatile for tasks like classification, regression, and clustering.
