Kerneltyp

Kerneltyp refers to the class or category of a kernel function used in kernel-based methods in statistics, machine learning, and related areas. In these contexts, a kernel is a function that computes the similarity between pairs of input objects, enabling algorithms to operate in a high- or infinite-dimensional feature space without an explicit mapping.

Common kernel types include:

- Linear kernel: K(x, y) = xᵀy, equivalent to applying a linear model in the input space.

- Polynomial kernel: K(x, y) = (α xᵀy + c)^d, allowing the capture of interactions up to degree d.

- Radial basis function (Gaussian) kernel: K(x, y) = exp(-γ‖x − y‖²), offering flexible, smooth nonlinear transformation.

- Sigmoid kernel: K(x, y) = tanh(κ xᵀy + θ), inspired by neural networks.

Key properties often considered for Kerneltyp include positive semi-definiteness and compliance with Mercer's theorem, which ensures the kernel corresponds to an inner product in some feature space. The kernel trick enables algorithms to operate in that space implicitly, by computing only kernel evaluations rather than explicit feature mappings.

Selection and tuning of Kerneltyp depend on data and task. Linear kernels suit linearly separable problems, polynomial kernels capture interactions, and RBF kernels handle complex nonlinear relationships. Hyperparameters (degree for polynomial, gamma for RBF, coef0) are typically chosen via cross-validation.

Applications span many kernel-based methods, such as support vector machines, kernel ridge regression, kernel principal component analysis, and spectral clustering, where the chosen kernel type directly influences model capacity and performance.