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

- 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 trick** in Support Vector Machines (SVMs) allows the model to learn complex decision boundaries without explicitly transforming original data points into a new, high-dimensional feature space. Instead, a kernelized SVM computes these boundaries using only similarity calculations (such as dot products) between pairs of points, leaving the high-dimensional transformed feature representation implicit.

SVM Kernel Trick

What does SVM do to solve the linear inseparable problem:

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