The similarity between two points and the transformed feature space is an exponentially decaying function of the distance between the vectors and the original input space.
$$K(x, x') = e^{-\gamma||x - x'||^2}$$

Using this kernel, the linear decision boundary in the feature space corresponds to a non-linear decision boundary in the original input space.

Radial Basis Function (RBF) Kernel in SVM

RBF kernel: it is mainly used in the case of linear indivisibility. There are many parameters, and the classification results are very dependent on the parameters. Many people find the appropriate parameters through the cross-validation of training data, but this process is time-consuming. If the number of features is small and the number of samples in general, which is neither large nor small, the SVM with RBF kernel is selected.

Radial Basis Function (RBF) Kernel

- Radial Basis Function (RBF) Kernel
- Polynomial Kernel

University of Michigan - Ann Arbor

The kernel function in an SVM model calculates the similarity in the new feature space of two points in the original feature space.

The SVM Gaussian kernel function is more complicated than the linear kernel function model, and it is easy to overfit.

SVM Kernel Function

Popular SVM Kernel Functions

The kernel function does not transform the original data points to the new high dimensional feature space. Instead, the kernelized SVM can compute these more complex decision boundaries just in terms of similarity calculations between pairs of points in the high dimensional space where the transformed feature representation is implicit.

SVM Kernel Trick

What does SVM do to solve the linear inseparable problem:

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